In order to determine the relationships between the soil stiffness constants of cohesive modulus of deformation, friction modulus of deformation and soil constant value and the rolling resistance, a series of tests was conducted using two types of loam and clay loam soil textures at four moisture contents of 10, 20, 30 and 40% and five loading speeds of 1, 2, 3, 4 and 5 mm s–1. The results showed that all of the independent factors had a significant effect on the soil stiffness constants, so with increases in moisture content and loading speed, the soil stiffness constants of cohesive modulus of deformation, friction modulus of deformation and soil constant value varied significantly. The highest cohesive modulus of deformation and friction modulus of deformation values were obtained at a moisture content of 10% and loading speed of 5 mm s–1 in a clay loam soil. All parameters were significant in calculating the rolling resistance using Bekkers’ relationship. With increases in soil moisture content, the rolling resistance increased, while increasing the loading speed reduced the rolling resistance significantly. In general, the highest rolling resistance value of 16 887.1 N was obtained at a moisture content value of 40% and a loading speed of 1 mm s–1 in loam soil.