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Oscillatory activity in the beta range, in human primary motor cortex (M1), shows interesting dynamics that are tied to behaviour and change systematically in disease. To investigate the pathophysiology underlying these changes, we must first understand how changes in beta activity are caused in healthy subjects. We therefore adapted a canonical (repeatable) microcircuit model used in dynamic causal modelling (DCM) previously used to model induced responses in visual cortex. We adapted this model to accommodate cytoarchitectural differences between visual and motor cortex. Using biologically plausible connections, we used Bayesian model selection to identify the best model of measured MEG data from 11 young healthy participants, performing a simple handgrip task. We found that the canonical M1 model had substantially more model evidence than the generic canonical microcircuit model when explaining measured MEG data. The canonical M1 model reproduced measured dynamics in humans at rest, in a manner consistent with equivalent studies performed in mice. Furthermore, the changes in excitability (self-inhibition) necessary to explain beta suppression during handgrip were consistent with the attenuation of sensory precision implied by predictive coding. These results establish the face validity of a model that can be used to explore the laminar interactions that underlie beta-oscillatory dynamics in humans in vivo. Our canonical M1 model may be useful for characterising the synaptic mechanisms that mediate pathophysiological beta dynamics associated with movement disorders, such as stroke or Parkinson's disease.