ESDU 78035 is a comprehensive review covering all possible conformal or non-conformal contact shapes; circular@ rectangular and elliptical. Curves are given that enable in each case the contact dimensions to be found@ the maximum surface stresses to be estimated@ and the maximum sub-surface shear stress to be calculated together with the depth at which it occurs. The full theory is also developed and the equations from which the curves were derived are included. To ease the application of the curves a calculation sheet is provided and its use is demonstrated with two practical worked examples. The method requires a knowledge of certain material properties and a table giving them for various metals@ ceramics and plastics is provided. See also ESDUpac A9434 in the Mechanisms or Tribology Series for a Fortran program providing solutions to this problem. NOTE: ESDU 78035 is still at Amendment C in the Tribology and Stress and Strength Series.