One of the intrinsic features of skin and other biological tissue is the high variation in the mechanical properties across individuals and different demographics. Mechanical characterization of skin is still a challenge because need for subject-specific in vivo parameters prevents us from utilizing traditional methods, e.g., uniaxial tensile test. Suction devices have been suggested as the best candidate to acquire mechanical properties of skin non-invasively, but capturing anisotropic properties using a circular probe opening - which is the conventional suction device - is not possible. On the other hand, non circular probe openings can drive different deformations with respect to fiber orientation, and therefore could be used to characterize the anisotropic mechanics of skin non-invasively. We propose the use of elliptical probe openings and a methodology to solve the inverse problem of finding mechanical properties from suction measurements. The proposed probe is tested virtually by solving the forward problem of skin deformation by a finite element (FE) model. The forward problem is a function of the material parameters. In order to solve for the inverse problem of determining skin properties from suction data, we use a Bayesian framework. The FE model is an expensive forward function, and is thus substituted with a Gaussian process metamodel to enable the Bayesian inference problem.