The free fall of short cylinders and rectangular prisms through polymer solutions of different measure of shear-thinning and elasticity has been investigated experimentally in the creeping flow region. The influence of the particle shape and the rheological behaviour of the liquid on the particle terminal velocity have been evaluated. A procedure based on the modification of the Stokes relationship for a Carreau model fluid have been proposed for the prediction of the terminal falling velocity of non-spherical particles. The suitability of the proposed procedure has been documented by good agreement between experimental and calculated terminal falling velocity data.