The first of the authors (B. R.) derived an expression for the pressure distribution inside a circular region with vanishing shear tractions and norma! displacements, due to the application of the forces distributed along the circumference on an elastic transversely isotropic half-space. This result is used to derive the relationships between the forces, moments and indentations for a punch acting on an elastic half-space. The results are given in terms of elementary functions. The influence of

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... an annular punch encircling a central punch is considered. The stress intensity factor of Mode I related to non-symmetric stress distribution in the vicinity of an external crack under generał surface loading, symmetric with respect to the crack piane, is also presented in terms of elementary functions.