This paper discusses axially symmetric contact problems of rigid punch and poroelastic foundation interaction employing Cowin-Nunziato linear poroelasticity model. It is assumed that the punch base has a flat or parabolic shape, and the contact friction is neglected. Using Hankel's integral transform the considered contact problem is reduced to a solution of a singular integral equation with unknown contact stress. To solve this integral equation, the collocation technique is used. In the case of parabolic punch, the contact pressure and the contact area were calculated. Then it is investigated the relation between the force applied to the punch and its displacement, which is one of the main characteristics in material properties determination by means of instrumented indentation method. A comparative analysis of considered quantities for various porosity values was carried out.