A 3D fruit tissue growth algorithm is presented based on the biomechanics of plant cells in tissues. The algorithm is able to generate realistic virtual fruit tissues. It was used to produce cell architectures of pome fruits with intercellular air spaces. The cell size and shape differences in pear cortex tissue and apple cortex tissue are obtained by implementing different maximum resting length of the cell walls and different cell wall stiffness (e.g., by including a degree of anisotropy) in the model. In addition to cell size and shape, the difference in the size of the intercellular air spaces and their connectivity is recognized in our model by implementing different pore formation mechanisms. The arrangement of different tissue layers which are observed from the skin to the cortex (epidermis, hypodermis and cortex) and particular features such as stone cells were also accounted for by our model. The algorithm was shown to produce cell architectures that are very similar to measured tissue structures of the pear and cortex tissue with intercellular air spaces. The resulting geometric models can be used in finite element simulations to study exchange processes within the fruit tissue and between the tissue and the surrounding environment. The geometric models can also be used to study coupled phenomena of moisture migration and tissue shrinkage in a multiscale approach. These approaches were demonstrated to be useful using our 2D version of the algorithm. The 3D version of the algorithm avoids many of the limitations of the 2D algorithm such as lack of intercellular air space connectivity in the 2D geometric models and hence, will help to better understand the exchange mechanisms.