This paper investigates the frictional contact problem of a layer indented by a rigid punch within the framework of the couple stress elasticity. It is assumed that the layer is homogeneous, isotropic, and fully bonded to a rigid substrate. The mixed-boundary value problem is converted using Fourier transform into a singular integral equation in which the unknown is the contact pressure between the layer and the punch. The integral equation is further derived for the flat and cylindrical punch case profiles, normalized and then solved numerically using the Gauss-Jacobi integration formula. The obtained results are first validated based on those published for the case of a frictionless contact problem of a half-plane indented by a rigid punch and solved within the context of couple stress theory. An extensive parametric study is then conducted to investigate the effect of several parameters on the contact stresses for the both the flat and cylindrical punch profiles. These parameters include the characteristic material length, the layer height, the friction coefficient, the indentation load, and the shear modulus.