UPDATE: Mea Culpa on my part. The painting below could very well be an illustration of the last stage of the siege, in which the Mexican forces infiltrated and overran the fort. In fact, several accounts place David Crockett's body in the courtyard in front of the chapel.
On February 23rd, 1836, the Mexican Cavalry under General Ramirez y Sesma entered the village of Bexar. Ramirez had been ordered to attack the Alamo fort at dawn, but a captured Texian scout convinced the Mexican commander of an awaiting Texian ambush. There were two attempts at parley made by Colonel Travis and Colonel Bowie (without each others' consent or cooperation), both of which were refused. The Mexicans demanded immediate surrender, which was rejected by Travis and Bowie. In the evening of the 23rd, the Mexican Army would encircle the fort, preparing for a siege that would begin at dawn on the 24th.
The illustration is by Howard David Johnson. The image features many famous elements of the battle, although how the image is presented doesn't jive with history. The well-known front facia of "The Alamo" is the front of the actual mission chapel, which faced toward the mission's courtyard, not outward. As well, the "Old Chapel" as it was known, was actually kind of "tacked on" to the then-current mission, and a barricaded earthworks had to be built from the front-right corner of the chapel to the walled main entrance to the south-east. This earthworks was considered the weakest point of defense, and was manned primarily by the Tennessee Volunteers during the siege.