ESDU 83010 uses slender body theory (independent of Mach number) to estimate the longitudinal lift distribution and pitching moment due to the oscillatory motion of slender bodies of revolution. A concise development of slender body theory for oscillatory motions of the body is included. Tabulated data apply to any body having a conical@ tangent ogive or ellipsoidal forebody in combination with a cylindrical afterbody The modes of oscillation considered are heave@ pitch about the body mid-point and a typical bending mode. The effects of body geometry and frequency of oscillation on the longitudinal lift distribution are shown graphically. The effects of body geometry on the airforce coefficients are also illustrated in graphical form. A set of equations is included to calculate flutter or inertia derivatives from the non-dimensional coefficients given in the tables. A Fortran program is provided on disc (uncompiled) in the software volume as ESDUpac A8310. In addition to covering the cases above it extends the method to bodies with paraboloidal@ or blunted tangent ogive or blunted conical forebodies. It also treats aft body boat-tailing. The input to and output from the program are explained and illustrated through five worked examples@ one of which relates to the flutter analysis of an underwing store@ and details of the warnings provided are given.