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The numerical simulation of two‐dimensional incompressible complex flows of viscoelastic fluids is presented. The context is one, relevant to the food industry (dough kneading), of stirring within a cylindrical vessel, where stirrers are attached to the lid of the vessel. The motion is driven by the rotation of the outer vessel wall, with various stirrer locations. With a single stirrer, both a concentric and an eccentric configuration are considered. A double‐stirrer eccentric case, with two symmetrically arranged stirrers, is also contrasted against the above. A parallel numerical method is adopted, based on a finite element semi‐implicit time‐stepping Taylor‐Galerkin/pressure‐correction scheme. For viscoelastic fluids, constant viscosity Oldroyd‐B and two shear‐thinning Phan‐Thien/Tanner constitutive models are employed. Both linear and exponential models at two different material parameters are considered. This permits a comparison of various stress, shear and extensional properties and their respective influences upon the flow fields generated. Variation with increasing speed of vessel and change in mixer geometry are analysed with respect to the flow kinematics and stress fields produced. Optimal kneading scenarios are commended with asymmetrical stirrer positioning, one‐stirrer proving better than two. Then, models with enhanced strain‐hardening, amplify levels of localised maxima in rate‐of‐work done per unit power consumed. Simulations are conducted via distributed parallel processing, performed on work‐station clusters, employing a conventional message passing protocol (PVM). Parallel results are compared against those obtained on a single processor (sequential computation). Ideal linear speed‐up with the number of processors has been observed.