We investigated linear and non-linear BOLD-grip force (GF) relationships in the brain using dominant (DH) and non-dominant hands (NDH). The NDH revealed widespread brain activations compared to DH, irrespective of GF. Looking at the BOLD-GF effects, both hands showed increased activations with increased GF within the contralateral M1 and ipsilateral anterior cerebellum. Non-linear BOLD-GF relationships (up to 4th order) were found, typically in posterior M1, premotor, sensory, parietal, and cerebellar areas. Finally, the consistent bilateral involvement of the cerebral and cerebellar areas suggests their involvement in error tracking or in synkinetic processes between DH and NDH.