Abstract: By means of the complex variable method, thisinvestigation addresses two kinds of contact problems in decagonalquasicrystalline materials. One kind of contact problem is the frictionalcontact problem, the other one is the adhesive contact problem.Particularly, the explicit expressions of the analytic functionscharacterizing the phonon and phason fields as well as the contact stressdistribution on the indenter are obtained for a flat indenter on a decagonalquasicrystalline half-space. The results show that 1) the contact stressesexhibit the real power type singularities - 1/2\pm \beta in the edge of the contact zone for the frictional contact problem with \beta determined bythe material constants of the quasicrystal and the static frictional factor;and 2) the contact stresses exhibit the oscillatory singularities -1/2 \pm \rm i \v in the edge of the contact zone for the adhesivecontact problem with \varepsilon determined by the material constants ofthe quasicrystal.