By combining lateral contact stiffness and friction measurements versus load obtained by modulated lateral force microscopy (MUM), the shear strength dependence on contact pressure can be studied. The adjustment of the elasticity contact theories to the experimental data also allows one to study the variation law of the friction force. Measurements on silicon oxide, mica, carbon fibers, and epoxy in ambient air and under a vacuum are presented. Two behaviors of the shear strength have been observed depending on the nature of the contact between tip and sample and on the environmental conditions. The shear strength presents either a linear dependence with the contact pressure or stays constant, i.e. independent of the pressure. When it depends on the pressure, the friction force apparently is proportional to the load; when it stays constant with varying pressure, the friction force is proportional to the contact area.