The torsion balance has been the experimental apparatus of choice for centuries, both in precision measurements of the Newtonian gravitational constant and in searches for weak anomalous interactions outside of gravity. If the form of the interaction is modeled, it is often possible to optimize the interacting bodies so that the apparatus has the greatest sensitivity to the interaction under study. Other researchers have applied this strategy in the case of the gravitational interaction between cylinders, and between a cylinder and sphere. Whereas their work focused on developing an analytical expression for the force between the masses, we present here a numerical method−Monte Carlo integration−which is general enough to aid in the design of bodies interacting under arbitrary potentials and with any desired geometric shape (as long as an accurate absolute value of the force is not needed). This numerical method is used to compute the gravitational torsion constant produced between an external hollow cylinder and sphere, and demonstrates the behavior studied previously through analysis. However, the main purpose for which we have used this numerical technique is in the design of interacting bodies used in a torsion‐pendulum search for interactions that depend on net intrinsic spin. We demonstrate how the method may be used to determine the optimum aspect ratio (l/r) of the polarized test masses, as well as the most sensitive orientation of the masses. Two different interactions are considered: the dipole–dipole interaction between two polarized bodies, and the monopole–dipole interaction between a polarized and unpolarized body. In the case of the monopole–dipole interaction, we also show how the numerical method can indicate which orientation between test bodies is most susceptible to a false signal caused by gravity.