The article deals with finding the optimum parameters of the elastic damping mechanism (EDM) in transmission of class 1,4 tractor. The tractor was used in structure of three various machine-tractor units and carried out the main agricultural operations: plowing, cultivation and cropping. EDM is intended for smooth start-off of the unit, decrease in dynamic loadings in transmission, protection of the engine against fluctuations of external loading. The indicator - "degree of the transmission transparency" is used for estimating the protective quality of the mechanism. The research was conducted by methods of experiment planning. The central composite plan of the second order for five factors has been chosen. The regression model expressing influence of key parameters of EDM on function of a response ("degree of transmission transparency") is received. The dependence of a response function from each factor, their mutual influence on the studied process is treated apart in details. The system of the differential equations in private derivatives has been received for finding the optimum values of factors and response function. The conclusion that the optimum value of the EDM parameters allow to increase quality of functioning of MTU on the main agricultural operations was made by results of the analysis of a computing experiment.