In this work an exact solution of the equations of the steady flow for a viscous incompressible fluid through a conical tube is presented when the Reynolds number is assumed small. The obtained solution is valid for every angleθ, with 0≤θ≤α, whereαis the angle of divergence of the conical tube and which is small, so that the flow must not be separated from the tube wall. The distributions of the dimensionless velocity and pressure gradient are found to be affected by the angle of divergence of the conical tube.