This paper presents a study of the deformations of the birch veneer layer of plywood composed of veneer sheets, each with a thickness of 1.4 mm. Displacements in the longitudinal and transverse directions were analyzed in each layer of veneer from the composition of the board. Cutting pressure was applied to the surface equal to the diameter of the water jet, located in the center of the laminated wood board. Finite element analysis (FEA) does not study the breaking of the material or its elastic deformation, but only what happens from a static point of view when maximum pressure acts on the board, which causes detachment of the veneer particles. The results of the finite element analysis indicate maximum values of 0.0012 mm in the longitudinal direction of the board located in the proximity of the application of the maximum force of the water jet. Additionally, in order to analyze the recorded differences between both longitudinal and transversal displacements, estimation of statistical parameters with 95% confidence intervals (CI) was applied. The comparative results indicate that the differences are not significant for the displacements under study.