Dynamic viscoelasticity of the systems having yield stress was measured using the raised cosine pulse (RCP) method by means of a cone‐plate type rheometer. The systems employed were mayonnaise and ketchup which are typical plastic materials. Influence of the amplitude of RCP strain on the convergence of the response stress was investigated. The response stress for a large RCP strain does not converge to zero. That is, the stress has a finite negative value still after a long time. In this case, the Fourier transformation of the response stress cannot be performed with a satisfied accuracy. On the other hand, the response stress converges to zero within a very short time for a small RCP stain and the frequency dependences of the dynamic moduli can be obtained, which are sufficiently congruent to them by the usual dynamic measurement.