In practical applications of transient electromagnetic methods, irregularity of the transmitting loop or current waveform makes the source an extended one. Since neglect of the effect of the extended source will cause some errors in both forward modeling and data interpretation, it makes great sense to calculate the responses that take this effect into account. For a spatially extended source over layered medium, step response is firstly calculated and taken as the basic response, then principle of reciprocity and the integral of the second kind are used to propose a new method that can compute the response based on the coordinates of the loop. For an extended source in time, an improved step-function summation method is proposed to deal with the contradiction between the precision of result and consuming of time. Comparisons with the published work have proved the validity and accuracy of our methods. The effect of the traditional approximations of the extended source is also investigated and some analysis for the numerical results is presented for advanced usage.