Some types of Josephson junctions such as long microbridges,S‐N‐Sjunctions, and junctions with a series palastic inductance are known to have nonsinusoidal current‐phase relations which can be approximated by linear‐periodic functions. In this paper the equivalent circuit equation of the resistively shunted junction model with linear‐periodic current‐phase relation is solved. The heights of zeroth and first constant‐voltage steps in the I‐V characteristics and the impedance at these steps are obtained analytically. This analysis shows that the impedance at the first step lies on a semicircle in the impedance plane with its center at the impedance of the zeroth step. The calculated impedance is compared with the experimental results by Claridgeetal. The theory presented here can explain some features of experimental results which differ considerably from predictions based on a sinusoidal current‐phase relation. Among these are the value of bias current corresponding to the center of the first step, and the appearance of ’’shoulders’’ in the imaginary part of the impedance at the first step.