The temperature dependence of lattice constants a and c of intermetallic compounds RMn2Ge2 (R=Sm, Gd) is measured in the temperature range 10-800K by using the x-ray diffraction method. The magnetoelastic anomalies of lattice constants are found at the different kinds of spontaneous magnetic transitions. The transversal and longitudinal magnetostrictions of polycrystalline samples are measured in the pulse magnetic field up to 25T. In the exteal magnetic field there occurs a first-order field-induced antiferromagnetism-ferromagnetism transition in the Mn sublattice, which gives rise to a large magnetostriction. The magnitude of magnetostrictions is as large as 10-3. The transversal and longitudinal magnetostrictions have the same sign and are almost equal. This indicates that the magnetostriction is isotropic and mainly caused by the interlayer Mn-Mn exchange interaction. The experimental results are explained in the framework of a two-sublattice ferrimagnet with the negative exchange interaction in one of the sublattices by taking into account the lattice constant dependence of interlayer Mn-Mn exchange interaction.