Determining the movement errors due to mechanical parts in computer numerical control devices is an important part of studying manufacturing and production. The propelling mechanical system of a computer numerical control device consists of engine, coupling, bearing, knot and leading rail. Each of these parts has an error value which causes manufacturing error in producing industrial parts. Although using closed-loop system has helped to solve this problem, still there are systems that use open loop. In this study, using Mooney–Rivlin model for flexible couplings, we calculated the errors due to the deformation of elastomeric medium, which is made of thermoplastic polyurethane. Using the ANSYS software, we simulated the three-dimensional model of medium to obtain elastic deformation. The loading type was chosen in terms of torque and stepper revolution of engine. At fixed 500 r/min, the effect of torque and engine stepper on the deformation was investigated, and the results obtained were compared with the simulations from experimental work on a computer numerical control desk with stepper 1.8 and 2.4 N m and ABBA coupling of model SRG-40C and ball screw of milled diameter 25 pitch 5 class C which showed a good confirmation.