The Thomas-Fermi approximation is applied to calculate the electron charge distributions of vacancies and edge dislocations in aluminium within the jellium model. The various factors affecting positron trapping, at crystal defects are discussed. A method is derived to evaluate the momentum dependent annihilation rate in a nonuniform electron gas. The calculation gives a value of 24% of the bulk value for the electron density at the centre of a vacancy. The annihilation characteristics are calculated for the trapped positron, and a good agreement with experimental results is established. An edge dislocation is described by a hollow core model. The hole radius of 0.85 AA is found to reproduce the experimental lifetime of positrons in deformed aluminium. The electron density at the centre of the dislocation core reduces to 37% of its value in the bulk material. The momentum distributions of the annihilation quanta are calculated for various dislocation orientations, and a remarkable anisotropy in angular correlation curves is found.