The paper addresses, with reference to the 3-parameter fluid, a method to extend constitutive laws for viscoelastic fluids from small to finite deformations. It relies upon the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts. Also care is taken that the second law of thermodynamics is satisfied in every admissible process. To demonstrate the capabilities of the model obtained, simple shear and uniaxial extensional flow are discussed. It turns out that essential effects of material behaviour, which have been observed experimentally, can be predicted by the model.