Three-dimensional numerical simulations of particle-laden flows have been performed using the Lattice Boltzmann method. The drag, lift and moment coefficients of differently shaped non-spherical single particles have been determined as a function of the angle of incidence and the Reynolds number under following flow conditions: a stationary particle in a uniform flow, a rotating particle in a uniform flow and a stationary particle in a linear shear flow. A new correlation formula for the standard drag coefficient of arbitrary shaped particles has been established using the numerical results and experimental data from the literature. This new correlation formula accounts for the particle orientation over the entire range of subcritical Reynolds numbers. Furthermore, the influence of the interaction between two spheres on their particle coefficients and the influence of turbulence on the motion of non-spherical particles have been determined. The relationships between the drag force, lift force and torque acting on particles and different flow conditions determined in this work shall make a contribution to the enhancement of the understanding of the motion of particles in laminar and turbulent flows. In addition, they can be used as a basis for the further development of Lagrange’ simulations of the motion of non-spherical particles.