Structure design and optimization of lattice structures not only need the conventional methods but also a flexible optimal shape modeling, generation, and developing technique for any customer query. Three-dimensional shape modeling today counts the specific needs for completeness of geometric queries of a design. To do this, computer-aided geometric designing is an area in which modeling of objects takes place and needs ongoing improvement to obtain smooth and accurate geometry. Recently, the partial differential equations were considered as an appreciable tool for geometric modeling than the traditional computer-aided designing algorithms, which is not studied enough. In this paper, a mathematical equation is developed from the solution of a six-order partial differential equation to model a 3D object shape with a set of mechanics-based boundary conditions. Based on the developed parametric analytical equation, the optimal size of the lattices, and the boundary equations of Body Centered Cubic and Face Centered Cubic structures, a solid shape is generated on computer graphics. Stress-based boundary equations (strength analysis), optimization results using MATLAB, and python programming were used to generate the 3D objects. As a comparative study, the analytical-based analysis had compared with the existing numerical analysis software’s (Ansys). The variation of results between the analytical and the numerical analysis for Body Centered Cubic (BCC), using Von Mises stress and maximum shear stress were 1.1% and 11% respectively. For Face Centered Cubic (FCC), the variations were 11.9% and 7.9% respectively. Considering some literature these values are acceptable which has a good correlation and the linearity of the analytical make it a preferable. Moreover, based on the stiffness per mass of the lattice structure, the BCC structure showed the best functionality on carrying higher load. Keywords: Computer-aided geometric designing; Lattice structure; Optimization; Parametric equation; Python programming; Partial differential equation; Shape generation.