PLAYA GIRON
The invasion begins
On April 17, the day following air strikes by the US led mercenaries, an invasion force consisting of more than 1500 men, landed on the southern coast of Cuba known as the Bay of Pigs ( Playa Giron ).
This area was chosen for the operation for two strategic reasons:  firstly, the area which is surrounded by swamps provided natural barriers, protection against government forces, secondly, this area with only two access roads - both in bad conditions - not only afforded additional protection to the brigade but gave them an opportunity to secure them against attack.
This brings up two important questions.  What was their mission?  Was it to set up camp and then to lead a "liberation army" into victory?
It is apparent that the intention of the brigade was not to march into Havana as a liberation army as Fidel Castro had done when he and his men overthrew Batista, but rather to have the US invade Cuba and then move in as an army of occupation.  In real terms the agenda of the invasion force was to secure and hold the area for 72 hours, long enough to be recognized by the US as a provisional government; and as such have the US govt. and some Latin American puppets intervene militarily.
That is why it was imperative for Cuba and it's forces to defeat the mercenaries in less than 72 hours.  And although the revolutionary army was not fully trained - it was barely two years old - and though badly equipped they were able to defeat the invasion force in a short time and thus avoid US intervention.
On December 1962, the Cuban government exchanged the 1,113 captured mercenaries for 53 million dollars worth in baby food and medicine - at least something good came out of this.  

Why did the Socialist government triumph and the invasion force so badly defeated?
First of all, the popular uprising that the US and the brigades were hoping for inside of Cuba never materialized.  Sure there were a few clandestine organizations, some of them armed groups like the bands in the Escambray mountains,  but they were never gained the support of the people as the new government was very popular; beside many of these groups lost support when some of them committed acts of terrorism against the Cuban people.
What is  important to understand is that Cuba's revolution was a response to the depressing social and economic conditions that existed at that time, as well as, a response against the neocolonial status of the island at that moment. What is just as important to remember is that the new government initiated concrete policies in the society to alleviate these conditions; concrete things were done; it was not mere rhetoric.  Among other things, rents were lowered, literacy was reduced, land was distributed to landless peasants.  Contrary to what you may be bought up to believe by the US ruling class, these policies were considered just and meaningful by the Cuban people, and as such the new government - los Revolucionarios - enjoyed overwhelming support.
Taking this within context meant that for the average Cuban the invasion force neither represented his interests or desires.  The exiles were seen not as liberators but rather as old masters who merely wanted to return to get their properties back and to return Cuba to the old corrupt ways. Ultimately,  the Cuban people's resolve and their total rejection of these people resulted in the defeat of this invasion force.
Some people have argued that the invasion failed because it was poorly planned and poorly equipped.  Don't be fooled.  The plan was sound; the area picked was ideal.  They were well equipped: 5 tanks, 1o motor armed vehicles, 19 mortars, 18 canons and a great quantity of bullets.  In matter of fact as briefly mentioned before it was the Cuban army which was poorly trained and poorly equipped.  Some of the Cuban troops were transported to the battle field by bus!
Their biggest mistake was that they underestimated the will and the resolve of the Cuban people.
Also, don't be fooled by the arguments within the US ruling class and the reactionary right wing Cuban - Americans that president Kennedy should have done more.  For Kennedy and the CIA knew fully well that the new Cuban govt. and Fidel Castro had the overwhelming  support of the Cuban people and as such that any direct support in the form of US intervention would have cost the lives and injuries of hundreds if not thousands on both sides.   Kennedy was not about to take action which would have caused  casualties and injuries to US soldiers; this is something which he wanted to avoid at the moment.
Lastly, the humiliating defeat of this US backed plan, which was a great defeat for the US ruling class, later pushed Kennedy into a corner.  Pushed to the edge, Kennedy, the ruling class and the CIA later considered and started to prepare for a direct US invasion of Cuba.  As result of this, a little more than a year later,  the US and the USSR were to square off in what is known as the missile crisis.  But that is another tale.                  
   
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