Key regulators in tissue-engineering processes such as cell culture and cellular organisation are the cell-cell and cell-matrix interactions. As mathematical models are increasingly applied to investigate biological phenomena in the biomedical field, it is important, for some applications, that these models incorporate an adequate description of cell adhesion. This study describes the development of a continuum model that represents a cell-in-gel culture system used in bone-tissue engineering, namely that of a cell aggregate embedded in a hydrogel. Cell adhesion is modelled through the use of non-local (integral) terms in the partial differential equations. The simulation results demonstrate that the effects of cell-cell and cell-matrix adhesion are particularly important for the survival and growth of the cell population and the production of extracellular matrix by the cells, concurring with experimental observations in the literature.