In Statistical Energy Analysis and Energy Flow Analysis models of connected beam systems, it is necessary to determine the power reflection and transmission coefficients of the structural joints. The use of a spectral element formulation to estimate the joint coefficients for any number of rigidly connected beams oriented at any angle in all three dimensions is presented. The longitudinal, transverse, and torsional wave types are modeled and assembled into beam elements. A force is applied to the system and the magnitudes of the transmitted and reflected waves are identified and used to calculate the joint's power reflection and transmission coefficients. Examples are presented to illustrate the procedure.