A method is presented for the pressure drop calculation during the viscoelastic fluid (VEF) flow through fixed beds of particles. It is based on the application of the modified Rabinowitsch-Mooney equation together with the corresponding relations for consistency variables. The course of dependence of dimensionless quantity coming from the momentum balance and expressing the influence of elastic effects on the suitably defined elasticity number is determined experimentally. The satisfactory validity of the approach suggested has been verified for pseudoplastic viscoelastic fluids characterized by the power-law flow model.