The drift velocities of spiral waves driven by a periodic mechanic deformation or a constant or periodic electric field are obtained under the weak deformation approximation around the spiral wave tip. An approximate formula is derived for these drift velocities and some significant results, such as the drift of spiral waves induced by a mechanical deformation with omega=3omega(0), are predicted. Numerical simulations are performed demonstrating qualitative agreement with the analytical results. (C) 2003 American Institute of Physics.