This article presents a Finite Element Algorithm (FEM) developed in Matlab environment in order to analyze the stability of shallow cylindrical composite shells including piezoelectric layers with ribbed reinforcement, subjected to static load. By the computer program, the authors examine different classes of problems to reveal the influence of factors such as reinforced ribs, the properties of the piezoelectric layer, and the structure of composite layers to the stability of the shell. Based on the results, appropriate selection of parameters will be given so that this kind of shells can be applied in technical fields like flying equipment, weapons, aerospace.