Slow viscous flow of rigid particles along a deformable tube of comparable diameter is considered as a possible model for some biological flows. Lubrication theory is assumed to be valid in the fluid region. The cylindrical tube is considered to be a thin elastic shell undergoing small deflections. The mean velocity of the flow is assumed to be maintained at a constant value by the application of a pressure difference over some length including the particle, or by an external force acting directly on the particle. Numerical results are obtained for the force required to maintain the motion and for the distribution of fluid pressure and thickness along the tube as a function of the diameter ratio, dimensionless velocity parameter and the shape of the particle. Effect of the bending resistance of the tube on the flow is also discussed.