An MRI simulation method, together with a corresponding computer program, using the k-space formalism has been developed. It uses a FFT algorithm to generate the ideal NMR signal from a user defined object. The k-space trajectory given by a pulse sequence is calculated. And it is used to select elements from the ideal NMR signal. This selection of elements mimic the sampling of the signal in an actual MRI experiment. During the sampling procedure changes in signal amplitude due to relaxation and excitation are introduced as well as signal phase changes due to movement or flow. Artifacts due to stimulated echoes and transversal magnetization that propagate through several repetition periods are also handled. The usefulness of the method is demonstrated by calculations using standard spin-echo sequence as well as modifications introduced in order to generate angiographical images and flow phase images. Further more a fast pulse sequence, echo planar imaging (EPI), is also simulated. The method is faster than previously presented ones. It is capable of generating images (128 x 128 matrix), including more than eight different T1 and T2 combinations, in less than 3 min on a standard 386/387 type IBM compatible PC.