This article addresses an original algorithm in topology optimisation of mechanical components to achieve a desired multi-dimensional stiffness using the level set method. As opposed to the main application of topology optimisation to maximise stiffness while minimising weight, this article focuses on a general formulation to reach a desired multi-dimensional stiffness. It is shown that a simple extension of previous formulations is not able to lead the optimisation procedure to the desired multi-dimensional stiffness. To fulfil this aim, two different loadings - force and displacement - are applied to the component/structure at the point with a desired multi-dimensional stiffness. The finite-element solution for the force (displacement) loading results in displacement (reaction force) at the point of applied force (displacement). When the topology of the component media converges, the resultant strain field for the force and displacement loadings will be the same; i.e. force (displacement) loading results in displacement (reaction force) at the point of applied loading satisfying F=K Δ. Here F and Δ are external force and displacement vectors, respectively. In addition, a new and effective energy-based constraint is proposed to avoid discontinuity in the component media.