The like-rubber O-ring gaskets are widely used in hydraulic and pneumatic equipments to ensure the sealing of the shaft, the pistons and the lids. The correct operation is due to the good tightening of the joint that generate a sufficient contact pressure able to confine the fluids inside rooms or to prevent their passage from one compartment to another. Several studies are carried out to model the O-ring behavior but without taking in account the effect of the relaxation and creep phenomena. In this article, an axisymmetric finite element model is proposed to study the O-ring relaxation during the first hours of its installation in the unrestrained axial loading case. The results of the numerical model are compared with an analytical approach results based on the classical Hertzian theory of the contact. The effects of the o-ring mechanical and geometrical characteristics are examined. The contact stress profiles and the peak contact stresses are determined versus the time relaxation in order to specify the working conditions thresholds.