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The basic objective of this thesis is to provide a practical method of computing the aerodynamic characteristics of slender finned vehicles such as sounding rockets, high speed bombs, and guided missiles. The aerodynamic characteristics considered are the normal force coefficient derivative, c(sub N(sub alpha)); center of pressure, bar-X; roll forcing moment coefficient derivative, c(sub l(sub delta)); roll damping moment coefficient derivative, c(sub l(sub p)); pitch damping moment coefficient derivative, c(sub mq); and the drag coefficient, c (sub D). Equations are determined for both subsonic and supersonic flow. No attempts is made to analyze the transonic region. The general configuration to which the relations are applicable is a slender axisymmetric body having three or four fins.