Circadian rhythms are archetypal examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are also affected by the cell’s mechanical environment. Here, we extend a standard biochemical model of circadian rhythmicity to include mechanical effects in a parametric manner. Using experimental observations to constrain the model, we suggest specific ways in which the mechanical signal might affect the clock. Additionally, a bifurcation analysis of the system predicts that these mechanical signals need to be within an optimal range for circadian oscillations to occur.