We analyze phase slip phenomena in one and two dimensional superconducting rings by solving the time-dependent Ginzburg-Landau equation. In the one dimensional case we show that the phase slipkinetics occurs simultaneously and consecutively depending on the dimensionless parameter u in the equation. In two dimensions there are two values ofcritical currents j c1 and j c2. When the local current is larger then j c1 the phase slip is similar to the one dimensional case.Kinetics is governed by kinematicvortices. When the local current exceeds j c2 value the vortex generation is governed by the Kibble-Zurek quench mechanism.