A new family of simple, analytic solutions of self-similarly expanding fireballs is found for systems with ellipsoidal symmetry and a direction dependent, generalized Hubble flow. Gaussian, shell like or oscillating density profiles emerge for simple choices of an arbitrary scaling function. New, cylindrically or spherically symmetric as well as approximately one dimensional hydrodynamical solutions are obtained for various special choices of the initial conditions.

PACS numbers: 24.10.Nz, 47.15.Hg