In bonding processes, the final distribution of the adhesive in the gap depends on the compressing normal load, velocity and kinematics, the adhesive properties, but above all on the initial adhesive distribution. The latter is also largely responsible for trapped air and the adhesive squeezes out at the edges. A model has recently been developed for the simulation of the flows during compression processes in adhesively bonded joints. This paper extends the aforementioned model towards shear rate-dependent viscosity, a phenomenon crucial for most industrial adhesives. Besides the assumption of a Newtonian fluid, approximations of a power-law and a Yasuda law are used. For this purpose, a further subordinate Newton method for determining the flow profiles is added to the existing model. Rheological measurements over a wide range of shear rates serve as a reference. For the verification, studies are performed on two academic examples: a rectangular, and a circular propagation. The results are compared with analytical solutions and CFD simulations. A very good agreement of pressure (deviations below 1.5%), and velocity profiles (deviations below 5%), for all scenarios and flow laws, was found. The long-term goal of this model development is the prediction of adhesive compression flows for complex application patterns.