This paper consists of two parts. In the first part a new and general formulation of the dynamical problems associated with the powered flight of variable-mass , flexible rockets with internal gas flow is presented. The formulation comprises six ordinary differential equations for the rigid-body motion and three partial differential equations for the elastic displacements. The equations are nonlinear and possess time-dependent coefficients. The formulation contains as special cases many of the rocket dynamics problems investigated heretofore, and should prove superior when several effects must be considered simultaneously. For a critical examination of the dynamical characteristics of variable-mass bodies, in the second part of the paper an analytical solution of the boundary-value problem with time-dependent coefficients associated with the longitudinal and transverse vibrations of an axially symmetric, variable-mass, spinning rocket is obtained. The paper scrutinizes the concept of normalmode vibration for boost vehicles with rapid mass variation.