We describe here a computational method to investigate the influence of dislocation core structure and coherency strains on γ-precipitate strengthening in nickel-based superalloys. The method is a combination of the Parametric Dislocation Dynamics (PDD), an analytical solution to the spherical inclusion problem and a computational form of the Peierls-Nabarro (PN) model. Using the method, we studied the role of the shape and core structure of super-dislocations in a γ'-matrix on the strengthening resulting from γ-precipitates. Earlier analytical solution to stacking fault strengthening predicts slightly lower critical resolved shear stress (CRSS) in the comparison with the present results. This is attributed to super-dislocation shape changes during its interaction with the γ-precipitate. On the other hand, the analytical solution to coherency strain strengthening provides considerably larger CRSS compared to the results of the present simulations. This is attributed to the spreading of the dislocation core during the interaction process. The dislocation core is found to spread widely so that its interaction with the γ-precipitate is much “softer” than considered in previous analytical solutions, where core spreading is not accounted for. This remarkable effect is a direct result of the core structure of dislocations interacting with precipitates, and must be considered in future dislocation dynamics simulations of precipitate strengthening. We finally discuss the combined strengthening effects of the two mechanisms.