  We propose a method to obtain new exact solutions of spinning p-branes in
flat space-times for any p, which manifest themselves as higher dimensional
Euler Tops and minimize their energy functional. We provide concrete examples
for the case of spherical topology S^{2}, S^{3} and rotational symmetry
\prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the
rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified
on the torus T^{m} . By double dimensional reduction the Light Cone
Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2}
membranes respectively. The solutions are interpreted as non-perturbative
spinning soliton states of type IIA-IIB superstrings.
