A general formalism based on the Green's function method is given for multi-electrode semiconductor lasers. The spatial hole burning effect is taken into account in this formalism. The frequency and intensity modulation properties of multi-electrode semiconductor lasers can be predicted using this theory. A general linewidth expression is given which includes contributions from spontaneous emission and carrier shot noise. This method is applied to two-electrode distributed feedback (DFB) and two-electrode distributed Bragg reflector (DBR) lasers. Experimental results for a two-electrode DBR laser are given and show a good agreement with the theoretical model. Moreover, the drive current noise of a tunable multi-electrode laser is shown to have an important influence on the measured lineshape and linewidth