General expressions for time-and surface-averaged radio frequency forces, affecting ions in closed toroidal devices, are obtained in this paper. Toroidal effects are included in these forces. These effects can, for example, be important to calculate Alfvén or fast wave forces in stellarators, spheromaks, or for toroidicity induced Alfvén wave eigenmodes ͑TAE͒ in axially symmetric tokamaks. The further simplification of obtained expressions should be fulfilled for the proper kind of rf waves and toroidal devices. It is hoped that these rf force expressions can, for example, be useful for the computer simulations of the transport barrier formation by Alfvén and fast waves in toroidal devices.