An earlier developed embedded Newtonian theory for prediction of the unsteady aerodynamics of hemisphere-cylinder-flare bodies has been extended to other hyperballistic geometries of general interest. Using generalized embedded Newtonian theory, the effect of Mach number is accounted for down to moderate supersonic speeds. The nose geometry can be described analytically or given in tabular form for a slender axisymmetric shape, which can include slope discontinuities. The "embedded" aft body can also be of a general shape, described by a series of conical segments, including the cylinder as a conical segment of zero slope.