A tortilla making machine comprising three mechanisms mainly for the process of manufacturing of tortillas and comprises a mixer that supplies and positions the portions of dough to be cooked, a moving press that flattens and shapes the portions of dough, and a cylindrical broiling oven that roast the product by using the curved surfaces on the inner and outer sides of the oven, that incorporates one or several burners or other source of heat in order to keep the surfaces and the inside volume of the oven at an accurate temperature to broil and complete the baking process on the inner side of the oven. The broiling oven is made up of metal tabs laid out along the curved surface of the oven that fold over, either towards the inner or to the outer side of the cylinder, this by gravity alone or supported by springs and closing and opening guides to allow the transition of the product to the inner side to be baked and to the outside to be unloaded.