We study the behaviour of Yukawa and Newtonian gravitational forces in a cubic box with fully periodic boundaries commonly encountered in N-body simulations of the structure formation. Placing a single gravitating body at the origin of coordinates, we reveal the scales at which non-negligible deviation from the Yukawa law occurs when the Newtonian approximation is employed. We discuss the results in terms of the corresponding physical distances today as well as earlier, back at the matter-dominated stage. Revisiting the problem for free boundaries, we also compare the periodic and plain gravitational forces for Yukawa-type interactions.