We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379-27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (MW 6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed. Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained by conventional kinematic source inversions. © Springer Science+Business Media B.V. 2008.