Humans are constantly exposed to air pollutants such as pollen, exhaust residues, microplastics, fabrics, aerosols or, as recently, ash particles from volcanic eruptions, which are rarely perfectly spherical. In order to reduce the impact of harmful particles or, on the contrary, to improve the targeted delivery of drugs, understanding the movement of complex-shaped particles in fluid flows is of key interest. Common models mainly use shape factors to account for deviations from spherical shape, but these often fail to accurately predict particle motion. We argue for a more accurate modelling of complex particles using a superellipsoidal shape approximation, which allows to cover a wide range of particle geometries. We investigate forces and torques on solid superellipsoidal particles in a Stokes flow using a numerical approach based on the boundary element method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows to the force and torque exerted on the particle. Expressions for the force and torque are proposed by introducing translational, rotational and deformation resistance tensors that capture each of the flow patterns individually. Based on these results, we present a model for translation and rotation resistance tensors for superellipsoidal particles. The developed model is implemented in OpenFOAM based on Lagrangian particle tracking. We first validate the proposed numerical scheme based on experimental and in-silico results from the literature, followed by a comparison of the effects of non-sphericity for some well-known flow cases, such as a lid-driven cavity and a simplified bifurcation. We show that the use of shape factor-assisted spherical or ellipsoidal approximations of the particles leads to insufficient accuracy of the particle trajectory calculation, whereas the newly derived superellipsoidal drag and torque models provide superior Lagrangian particle tracking accuracy over simplified non-spherical particle approximations. References: M. Štrakl, M. Hriberšek, J. Wedel, P. Steinmann and J. Ravnik. A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow. J. Mar. Sci. Eng., Vol. 10/3, pp. 369, 2022. J. Wedel, P. Steinmann, M. Štrakl, M. Hriberšek, J. Ravnik. Shape matters: Lagrangian tracking of complex nonspherical microparticles in superellipsoidal approximation. International Journal of Multiphase Flow, 2022