This study presents a surface roughness analysis of the mechanism of peristaltic flow in viscous fluids through a diverging cylindrical tube. The effects of different heights of surface roughness of the inner walls of a diverging tube have been included in the analysis. Formulation of the problem is done based on the continuity and momentum equations in a cylindrical coordinate system. A standard lubrication approach is adopted to simplify the formulations for exact solutions. The influence of surface roughness of the tube wall on flow velocity, pressure rise,flow rate, friction force and streamline patterns have been computed. Results suggest that the impact of roughness cannot be ignored during the peristaltic pumping of the fluid as a profound effect of roughness is seen on pressurerise and friction force. The basic peristaltic model presented by Shapiro et al in J. Fluid Mech. $37$, 799 (1969) is the special case of this model for zero surface roughness with unform channel. This analysis will provide a benchmarkfor various non-Newtonian pumping flow models with surface roughness analysis. The finding of the present model will also be utilised in developing the emerging health care pumping devices for transport phenomena.