For plane deformations generated by an arbitrary distribution of tractions applied in a small region on the boundary of an elastic half-plane, the rates-of-decay for displacements, stresses and strain energy density are obtained as functions of complexity of the load distribution. The rates-of-decay increase in proportion to the complexity of the load distribution; i.e., they increase with the order of the smallest nonvanishing moment of the traction distribution. In orthotropic materials the elastic moduli differ in two perpendicular directions of principal stiffness; in this case as the modulus ratio
E
2
/
E
1
{E_2}/{E_1}
increases, the angular distributions of the displacement and energy density fields become channeled towards the direction of the larger elastic modulus.