SymBRiM is a Python package to model bicycle-riders symbolically. It offers a modular and extendable framework that empowers users to easily compose a custom bicycle-rider model. These models are build from a library of components, such as knife-edge wheels or toroidal-shaped wheels. The components serve as the building blocks of the system. Leveraging the open-source Python package SymPy, a computer algebra system, SymBRiM allows the usage of SymPy's bodies and joints interface to modify the model and other tools to manipulate the equations. The equations of motion for the system are derived using Kane's method, which can be further analysed and used in simulation and optimization tasks.