Any force acting on a body can (a) produce a change in length - longitudinal (b) produce a change in volume - Volumetric (c) produce a change in shape without changing the volume - Shearing

Tensile stress – When a solid cylinder is stretched by two equal forces, applied normal to the cross-sectional area, the restoring force per unit area of the body is called Tensile stress

Compressive stress – When a solid cylinder is compressed under the action of forces, applied normal to the cross-sectional area, the restoring force per unit area of the body is called compressive stress

In both the above cases, as there is a change in length alone, it is called longitudinal stress