Vibration or bouncing of electrical contacts at closure is a reason of failure occurring in relays, contactors, circuit breakers and other electrical equipment due to arc erosion and welding. Experimentally observed bouncing of electrical contacts in vacuum circuit breakers cannot be satisfactorily explained by elastic restitution force or electrodynamic repulsion. This paper attempts to estimate the influence of metallic vapour pressure generated by arc in the contact gap on contact motion. The mathematical model describing these phenomena includes a non-linear differential motion equation for a movable contact piece, heat equations for anode and cathode (Axisymmetric Stefan's problem with two free boundaries for melting and evaporation), a differential equation for the arc column, and non-linear algebraic equations for near-electrode regions. The special method of majorant functions is applied for the solution of this problem. It is found theoretically and confirmed experimentally that the vapour force at contact bouncing is sometimes comparable and may be greater than the contact spring force even in vacuum. Some aspects of resonance phenomena, when the frequency of mechanical oscillations is close to the frequency of alternative current are also discussed.