The article develops a Lagrangian based model for a two-link mechanism termed a microscallop, moving in a low Reynolds number environment in a shear thinning/thickening fluid. The modelling proceeds through the conventional Lagrangian construction for a two-link mechanism and then goes on to model the external fluid forces using empirically based models for viscosity to complete the dynamic model. The derived model is then simulated for different initial conditions and key parameters of the shear thinning/thickening fluid - mainly time independent fluids such as shear thinning and shear thickening fluids, and the results are corroborated with existing experimental results on a similar mechanism under identical conditions. The resulting analytical model with complex nonlinearities is then simplified for further control-theoretic analysis. A few simulation-verified simplifications are introduced to study the accessibility of the system at various initial states. The final goal is to determine control algorithms for such a system to enable manipulation in its fluid environment.