In this paper, the design optimization of the linear hydraulic motor plunger from horizontal Hydraulic Press – 2 MN is presented. The analysis of linear the hydraulic motor plunger of horizontal Hydraulic Press – 2 MN was made for determination of stresses, displacements, deformations, buckling and the factors of safety distribution. A three-dimensional model of the linear hydraulic motor plunger was generated based on the designed data. Finite element analysis was performed using COSMOSWorks software. The simulation results were evaluated and compared to the experimental data. Results show that the established FEM model provides useful information for the plunger optimal design.