Lekner [ Molec. Simul. 20, 356 ( 1998)] and Sperb's [ Molec. Simul. 13, 189 ( 1994)] work on the evaluation of Coulomb energy and forces under periodic boundary conditions is generalized. So, now it should be possible to use a triclinic unit cell in simulations in 3D rather than just an orthorhombic cell. The expressions obtained are in a similar form as previously obtained by Lekner and Sperb for the especial case of an orthorhombic cell.