This investigation deals with characteristics of rocking vibration of rigid block subjected to the horizontal harmonic excitations. Nonlinear rocking system may include minute changes of system parameters, such as friction and restitution coefficients depending on contact conditions between the block and the base, and friction force that may vary as the block moves. This paper is the first part of the examination how minute changes of the above system parameters are related with minute changes of friction coefficients. A numerical analysis program has been developed to solve nonlinear motion equations for rocking motion of a rigid block subjected to horizontal base excitation. Natural changes of friction coefficient are simulated by random numbers with a normal probability distribution. Analytical results have shown that rocking responses are very sensitive to small changes of friction conditions between the block and the base. Minute changes of the friction coefficients make rocking response unstable and greatly change the response distribution itself. Because of the dynamic nature of friction coefficients changes, experimental rocking responses are not recurring.