Shells structures are very important for various engineering fields, and those were used in many applications of engineering. Axisymmetric Shells of Revolution structures (ASR) are used as dome type of roofs, for various functions such as houses of worship, stadium, cinemas, galleries, tanks, and other. In Structural design, it is necessary to obtain an appropriate geometric shape for the structure, so that it can carry the imposed loads safely and economically. This can be achieved using Structural Optimization (SO) procedures. Optimization of shell structures can result not only in improved designs, but also in a large saving of material. The main objective of this research work is to carry out SO for ASR by using Finite Element Method (FEM) and SAP-2000 programme. This work aims to arrived at the optimum case of structures with respect to rise, thickness, and shape, optimization treating them separately or by combining them. The outcome of this thesis has been the generation of new research information on performance characteristics of ASR that will facilitate improved designs of shells with better choice of shapes and enhanced levels of economy and performance.