Cone-and-plate rheometers are widely used to measure viscometric parameters in incompressible viscous flow problems. During these measurements it is implicitly assumed that the flow regime inside the rheometer is purely unidirectional and isothermal. Such assumptions are not in general true. In this paper we describe a Galerkin finite element model for the simulation of the flow patterns in cone-and-plate viscometer experiments. The results of our investigation show that the flow in these measurements is not unidirectional and noticeable secondary flows are sometimes present. The aim of this paper is not however, to dismiss cane-and-plate viscometry as unreliable. Our objective is to study various factors which either by giving rise to secondary flows or by causing significant non-uniform temperature distributions inside the viscometer influence the results of the measurements. These include edge effects, non-linear material behaviour, such as shear thinning and viscoelasticity, and viscous heat generation during the experiment. In some cases such factors are quite significant and they result in non-uniform stress distribution on the cone surface. Due to the complexity of the phenomena a direct experimental measurement of the degree of flow domain non-uniformity caused by each one of the described factors is not possible. The quantitative evaluation of the non-uniform stress fields via a mathematical model however, can be used to estimate the viscometry errors in rotating cone rheometers. We have developed an algorithm in which the simulated stresses are used to modify and improve the experimental viscometric results obtained by the cone-and-plate method.