The nonlinear propagation of low frequency electrostatic shock waves in a multi-component dusty plasma has been theoretically investigated. The reductive perturbation method has been employed in order to derive the Burgers equations. The stationary solution of Burgers equation has been obtained and numerically analyzed for different plasma system. The results, which have been found in thermal plasma are pointed out as follows: i) the basic features of the shock waves are found to be significantly modified by the effects of dust kinematic viscosity; ii) Both polarity (positive and negative potential) shock waves are found to exists.