Peripheral nerves carry electrical impulses from the brain and spinal column to the rest of the body allowing for movement and the transmission of sensory information. It is estimated that 2.8% of trauma patients suffer peripheral nerve damage, however, the gold standard treatment, of nerve autograft, is estimated to have a success rate of 40-50% depending on the scale of the injury. Treatments are being developed which use bioengineered conduits to promote axon regrowth. For this to be an effective treatment the implant must match the mechanical properties of the undamaged nerve. The mechanical properties of peripheral nerves can be experimentally measured however these properties are difficult to obtain from cadavers due to the use of fixatives. In this work we build a multiscale biomechanical model to describe the mechanical properties of peripheral nerves using geometrical data which can be obtained from cadavers. Using asymptotic homogenisation, we construct a semi-analytic model for the effective macroscale behaviour of fibre supported linear elastic cylinders. Implementing this model using COMSOL Multiphysics we see our model is consistent with analogous models in the literature. We use our model to investigate a range of starting assumptions on the microscale mechanical properties of the composite material. To more accurately consider the mechanical properties of peripheral nerves a layered fibre supported model is also considered to emulate the hierarchy of the peripheral nerve. Experimental data is used to parametrise the model and similar trends are observed to what is seen in experiments. Finally, we consider the mechanical properties of tissue-engineered repair conduits currently in development. Different internal geometries must be considered to promote cell growth. We consider how we may use the mechanical properties of nerves to reduce the number of degrees of freedom that must be considered by researchers optimising axonogenesis or vascularisation through these designs.