The cerebellum has been hypothesized to provide internal models for limb movement control. If the cerebellum is the site of an inverse dynamics model, then cerebellar neural activity should signal limb dynamics and be coupled to arm muscle activity. To address this, we recorded from 166 task-related Purkinje cells in two monkeys performing circular manual tracking under varying viscous and elastic loads. Hand forces and arm muscle activity increased with the load, and their spatial tuning differed markedly between the viscous and elastic fields. In contrast, the simple spike firing of 91.0% of the Purkinje cells was not significantly modulated by the force nor was their spatial tuning affected. For the 15 cells with a significant force effect, changes were small and isolated. These results do not support the hypothesis that Purkinje cells represent the output of an inverse dynamics model of the arm. Instead these neurons provide a kinematic representation of arm movements.