The relationship between the BOLD response and an applied force was quantified in the cerebellum using a power grip task. To investigate whether the cerebellum responds in an on/off way to motor demands or contributes to motor responses in a parametric fashion, similarly to the cortex, five grip force levels were investigated under visual feedback. Functional MRI data were acquired in 13 healthy volunteers and their responses were analyzed using a cerebellum‐optimized pipeline. This allowed us to evaluate, within the cerebellum, voxelwise linear and non‐linear associations between cerebellar activations and forces. We showed extensive non‐linear activations (with a parametric design), covering the anterior and posterior lobes of the cerebellum with a BOLD‐force relationship that is region‐dependent. Linear responses were mainly located in the anterior lobe, similarly to the cortex, where linear responses are localized in M1. Complex responses were localized in the posterior lobe, reflecting its key role in attention and executive processing, required during visually guided movement. Given the highly organized responses in the cerebellar cortex, a key question is whether deep cerebellar nuclei show similar parametric effects. We found positive correlations with force in the ipsilateral dentate nucleus and negative correlations on the contralateral side, suggesting a somatotopic organization of the dentate nucleus in line with cerebellar and cortical areas. Our results confirm that there is cerebellar organization involving all grey matter structures that reflect functional segregation in the cortex, where cerebellar lobules and dentate nuclei contribute to complex motor tasks with different BOLD response profiles in relation to the forces. Hum Brain Mapp 38:2566–2579, 2017. © 2017 Wiley Periodicals, Inc.