The author measured the stress generated in situ by a tamper (78kg) while compacting cohesive soil (Cr.) and sand (Fr.) of a fill-type darn, and discussed these theoretical background. Results are as follow. 1) The model of the behavior of tamper-ground systems are expressed by the linear models of 3rd, 2nd and single degree of freedom as eq. (1)-(4), eq. (12)-(13) and eq. (17), shown Fig. 1. 2) By supposing a soil prism region where the stress works effective for compaction, the stress are calculated from the theory of the strain energy. The height of soil prism is double of the depth generating the stress which is one half of the surface stress. A is a contact area in eq. (28). 3) Measured stresses in Fr. are larger than in Cr.. Quasi-dynamic forces are caluculated at 3.6-5.6 kg/cm2 from these values. 4) Substituting the values K, M, E and a, measured by field and laboratory tests, into the equations in 1), a theoretical force is obtained but extraordinary in comparison with measure values. However using equations in 2), theoretical stresses are calculated at 3.8-5.2 kg/cm2 which almost coincide with experimental results. 5) Ground characteristics such as of soil, water content and density effect the stress generated by a tamper.