Pressure gradient driven, laminar, fully developed pulsating pipe flows have been extensively studied by various researchers and the data for the resultant flow field are available in a number of publications. The present paper, however, concentrates on related flows that are mass flow driven, i.e., the flows where the mass flow rate is prescribed as and is periodically varying in time. Sinusoidal and triangular mass flow rate pulsations in time are analytically considered in detail. Results of experimental investigations are presented and are complemented by data deduced from corresponding analytical and numerical studies. Overall, the results provide a clear insight into mass flow rate driven, laminar, fully developed pulsating pipe flow. To the best of the authors’ knowledge, flows of this kind have not been studied before experimentally, analytically and numerically.