The quasi-static frictional contact problem of a rigid rounded punch sliding over a bidirectionally graded half-plane is treated within the framework of plane-strain elasticity. The material heterogeneity in the half-plane is assumed to entail independent shear modulus variations along the depth and longitudinal directions in terms of exponential functions. In-plane field variables are converted through the Fourier transform method and subsequently reduced to a Cauchy singular integral equation (SIE) as a function of the unknown contact stress. The SIE is solved using a collocation approach on the roots of the Chebyshev polynomial of the first kind. A finite element approach (FEA) is also implemented for the same contact problem employing the homogeneous finite element method and the augmented Lagrange algorithm in the environment of a structural analysis software. Besides the verification results generated by the foregoing techniques, the effects of such factors as the friction coefficient and the degree of material heterogeneities are also addressed on the contact stress, the in-plane tensile stress, the normal contact force and on the centerline position of the punch. The bidirectional gradation is evidently shown superior to the conventional one-directional gradation, as far as their potentials are considered for the alleviation of the contact-induced failure risks.