Properties of rate- and state-dependent friction laws are examined through numerical simulations. Among several versions of the rate- and state-dependent friction laws, we use the slowness law, the slip law, and the composite law. The last was recently proposed by Kato and Tullis (2001) for better explaining experimental observations of rock friction in the laboratory. Two kinds of simulations are done. One is for cyclic stick-slip motion of a single degree of freedom spring-block system. The other is for seismic cycles at a subduction zone, where a 2D model of uniform elastic half-space is used. Assuming the same values of friction parameters, we compare the simulation results for the three friction laws. From the two kinds of simulations, we find that the recurrence interval of simulated earthquakes is the longest, and the magnitude of preseismic sliding is the smallest, for the composite law.