A computational study of discrete 'cell-centre' approaches to modelling the evolution of a collection of cells is undertaken. The study focuses on the mechanical aspects of the tissue, in order to separate the passive mechanical response of the model from active effects such as cell-growth and cell division. Issues which arise when implementing these models are described, and a series of numerical mechanical experiments is performed. It is shown that discrete tissues modelled this way typically exhibit elastic-plastic behaviour under slow compression, and act as a brittle linear elastic solid under slow tension. Both overlapping spheres and Voronoi-tessellation-based models are examined, and the effect of different cell-cell interaction force laws on the bulk mechanical properties of the tissue is determined. This correspondence allows parameters in the cell-based model to be chosen to be compatible with bulk tissue measurements.