Flexibility factors and stress indices for elbows and curved pipe loaded with an arbitrary combination of in-plane, out-of-plane, and torsional bending moments are developed for use with the simplified analyses procedures of present-day design codes and standards. An existing analytical method was modified for use in calculating these factors: the equations were programmed for the IBM-360 computer and computed results were compared with experimental data to establish the adequacy of the modified method. Parametric studies were then performed to obtain desired information. The results are presented in both tabular and graphical form. Approximate equations of best fit, developed from the tabulated values, are presented in a form which can be used directly in the codes and standards. The present equations are slightly more conservative than the ones in current use. However, experimental and analytical studies now in progress may indicate further modifications in the stress indices and flexibility factors for elbows.