Dynamic slip pulse propagation along a material interface is of great interest because many faults are known to lie along material interfaces and such interfaces may cause pulse‐like ruptures. This subject has been extensively studied numerically over the last two decades. It has not, however, been studied very thoroughly from an analytical standpoint, although analytical studies would complement numerical ones. In particular, an analytical solution for removing stress singularities has not yet been obtained, even after an asymptotic analysis. In this article, we employ three physically plausible conditions in our theoretical modeling: (1) arbitrary propagation speeds in the sub‐Rayleigh range, (2) a slip‐weakening friction law, and (3) boundedness of stress. We can construct an analytical solution under these conditions, and as a result of our parameter study, we determine the dependence of slip‐weakening distance and the ratio of process zone size to pulse length on rupture direction and velocity. These results enable us to discuss a mechanism for limiting rupture velocity and estimating the slip‐weakening distance in seismic inversion analyses.