A new mathematical model of velocity distribution of single-phase fluid flow in packed beds was developed by assuming the flow characteristic is a combination of a continuous and a discontinuous systems of fluids between voids in the bed. The model can be applied for both compressible and incompressible fluids. The validity of the model has been checked using the measured data at inside and downstream of the bed. The agreement between measured data and the results predicted by the model is good. The model compares favourably with previous models in terms of accuracy and simplicity and does not require new empirical constants.