A novel two-dimensional finite volume procedure is described in detail for the analysis of incompressible linear elastic body, the volume conservation for each volume form a constrain equation is added to governing equation of linear elastic body, the procedure of discretize governing equations using bi-linear quadrilateral elements is given in detail. The discrete equation contains displacement and hydrostatic pressure as unknown variable, and the hydrostatic pressure is storied at the center of the element and assumed to be constant within each element. The developed procedure is tested on two linear elastic plane strain benchmark problems of impressible material, and then compared with analytical results. In addition, no locking problem is encountered as the poisson’s ratio equal to 0.5 which is a common problem in FEM, the simulation results show that this FVM can obtain an accurate and stable numerical solution under mesh refinement.
