Cycloidal gears make up the main working unit of hydraulic gerotor machines. In the article, a question of a more efficient application of plastics in building the gears is discussed. The discussion is based on a numerical strain analysis which was done by means of the finite elements method. The stress and deformation values in the operating cycloidal gears were specified. The numerical analysis was carried out in two stages in order to determine the optimum gear tooth profile. The profile depends on the tooth height and on the tooth correction coefficient. At the first stage, the optimum tooth height coefficient was calculated. Having determined the optimum value , the analysis was continued, and at the second stage, the optimum correction coefficient v for the gears at an earlier selected constant value was defined. The analysis results were useful in selecting parameters for determining the geometrical characteristics of the cycloidal gears. The parameters were then used in defining the most suitable tooth profile for the hydraulic machine featuring the cycloidal gears.