The laminar flow of an unsteady viscous liquid with uniform distribution of dust particles through a circular cylinder under the influence of exponential pressure gradient has been investigated. The governing equations are reduced to second order differential equation with suitable substation and Finite difference technique is applied to discritize the governing equations. The system of difference equations are then solved by MATLAB. Velocity distribution is shown graphically and it is also observed that velocity decreases with the decrease of ‘n’. The velocity profiles shrink with respect to time t. The dust particle velocities slightly more than clean dust particles for all value of ‘n’ and time t.