This research deals with the problem of modelling the orbit and attitude motion of uncontrolled manmade objects in orbit about the Earth, which tumble due to the natural influences of the near-Earth space environment. A mathematical, physics-based and computational approach is taken to model the forces and torques that drive the orbit and attitude evolution of such objects. The main influence modelled is solar radiation pressure (SRP), which is the interaction of solar electromagnetic radiation with the surface of an object, leading to both forces and torques that influence the orbital and attitude motion. Other influences, such as the gravitational field of the Earth, are also modelled.