In order to use a parallel device fur machine tool feed mechanism, it is very important to analyze its stiffness over the workspace. Generally, the stiffness of a rod varies with its length. In this paper, the stiffness of the leg is modeled as a linear function. With the linear stiffness model, the methods that can determine stiffness bounds and max/min stiffness directions are presented utilizing eigenvalues and eigenvectors of the stiffness matrix. The stiffness variation along a tool-path and stiffness mapping over a workspace are presented with cubic-shaped parallel device which is originally designed for machine tool feed mechanism.