Numerous experimental studies have attempted to determine the optimal properties for a scaffold for use in bone tissue engineering but, as yet, no computational or theoretical approach has been developed that suggests how best to combine the various design parameters, e.g. scaffold porosity, Young's modulus, and dissolution rate. Previous research has shown that bone regeneration during fracture healing and osteochondral defect repair can be simulated using mechanoregulation algorithms based on computing strain and/or fluid flow in the regenerating tissue. In this paper a fully three-dimensional approach is used for computer simulation of tissue differentiation and bone regeneration in a regular scaffold as a function of porosity, Young's modulus, and dissolution rate--and this is done under both low and high loading conditions. The mechanoregulation algorithm employed determines tissue differentiation both in terms of the prevailing biophysical stimulus and number of precursor cells, where cell number is computed based on a three-dimensional random-walk approach. The simulations predict that all three design variables have a critical effect on the amount of bone regenerated, but not in an intuitive way: in a low load environment, a higher porosity and higher stiffness but a medium dissolution rate gives the greatest amount of bone whereas in a high load environment the dissolution rate should be lower otherwise the scaffold will collapse--at lower initial porosities however, higher dissolution rates can be sustained. Besides showing that scaffolds may be optimised to suit the site-specific loading requirements, the results open up a new approach for computational simulations in tissue engineering.