We present a numerical model of a contactless test commonly used to assess the biomechanics of the human cornea. The test, consisting in a rapid air jet applied to the anterior surface of the cornea, is controversial. Although the numerous studies documented in the literature have not been able yet to clarify its relevance as a diagnostic tool, the test has the potential to be combined with inverse analysis procedures to characterize the parameters of numerical models of the cornea. With the final goal of employing the air puff test in advanced material identification algorithms, here we propose to model the cornea with standard finite elements and the fluids filling the anterior chamber of the eye with a meshfree discretization. The interaction between moving fluids and deforming cornea is accounted for by modifying the interface boundary conditions of both fluid and solid. The proposed model represents the first fully 3D example of an aqueous-cornea fluid-solid interaction analysis which uses a robust meshfree approach for the fluid. Although we restrict our scope to isotropic nonlinear materials, numerical results confirm the undeniable importance of including internal fluids in the simulation of the air puff test. Thus the proposed approach stands as a procedural paradigm for the identification of the mechanical parameters of the human cornea.