Based on the Boussinesq formula, exact formulae are derived for the vertical stress beneath the corner of an arbitrarily shaped triangular surface region subjected to vertical pressures with a uniform, linear, or quadratic distribution. These formulae are the basis of a proposed analysis technique in which any arbitrarily shaped loading region is approximated by a set of triangular regions. Computer algorithms that take advantage of the highly repetitive, yet simple, mathematical operations can readily be implemented on the computational facilities currently available to most engineers.Key words: triangular or arbitrarily shaped load regions, vertical stress distribution, computer solution.