  We construct a class of solutions to the Einstein's equations for dimensions
greater than or equal to six. These solutions are characterized by a
non-trivial warp factor and possess a non-compact extra dimension. We study in
detail a simple model in six dimensions containing two four branes. One of each
brane's four spatial directions is compactified. The hierarchy problem is
resolved by the enormous difference between the warp factors at the positions
of the two branes, with the standard model fields living on the brane with
small warp factor. Both branes can have positive tensions. Their positions, and
the size of the compact dimension are determined in terms of the fundamental
parameters of the theory by a combination of two independent and comparable
effects---an anisotropic contribution to the stress tensor of each brane from
quantum fields living on it and a contribution to the stress tensor from a bulk
scalar field. One overall fine tuning of the parameters of the theory is
required ---that for the cosmological constant.
