In support of the InSight mission in which two instruments (the SEIS seismometer and the HP3 heat flow probe) will interact directly with the regolith on the surface of Mars, a series of mechanical tests were conducted on three different regolith simulants to better understand the observations of the physical and mechanical parameters that will be derived from InSight. The mechanical data obtained were also compared to data on terrestrial sands. The density of the regolith strongly influences its mechanical properties, as determined from the data on terrestrial sands. The elastoplastic compression volume changes were investigated through oedometer tests that also provided estimates of possible changes in density with depth. The results of direct shear tests provided values of friction angles that were compared with that of a terrestrial sand, and an extrapolation to lower density provided a friction angle compatible with that estimated from previous observations on the surface of Mars. The importance of the contracting/dilating shear volume changes of sands on the dynamic penetration of the mole was determined, with penetration facilitated by the ∼1.3 Mg/m3 density estimated at the landing site. Seismic velocities, measured by means of piezoelectric bender elements in triaxial specimens submitted to various isotropic confining stresses, show the importance of the confining stress, with lesser influence of density changes under compression. A power law relation of velocity as a function of confining stress with an exponent of 0.3 was identified from the tests, allowing an estimate of the surface seismic velocity of 150 m/s. The effect on the seismic velocity of a 10% proportion of rock in the regolith was also studied. These data will be compared with in situ data measured by InSight after landing.