Dieterich proposed a time and velocity‐dependent friction law that explains his experimental data for velocity‐controlled rock‐friction tests and provides some physical insight on the mechanics of stick‐slip. This law, however, is not formulated in a differential or integral form. As a consequence, numerical problems arise in applying it to the cases when the slip velocity varies continuously with time. We introduce a differential‐equation reformulation of the friction law for which the law proposed by Dieterich is a special solution. This new formulation permits precise and more generalized solution for frictional response and is of value for numerical modeling of laboratory experiments and fault mechanics in general. Two examples of solution, one for velocity‐controlled rigid slider, the other for traction‐controlled rigid slider, are given for illustration. Numerical results are compared with those obtained by Dieterich's original formulation. This paper is not subject to U.S. copyright.