A novel contact model is presented to efficiently solve a face-mask contact problem by using the finite element (FE) method for the optimized design of a custom facial mask. Simulation of contact pressure for various mask designs considering material properties of the face allows virtual evaluation of the suitability of a mask design for a person's face without conducting empirical measurement of the face-mask contact pressure. The proposed contact model is accomplished by combining three approaches to reduce the calculation cost of simulating the face-mask contact: (1) use of a simplified and modifiable mask model that applies a spline curve to design points; (2) reduction of the FE model of the face by applying static condensation; and (3) application of a contact assumption that uses the Lagrange multiplier method. A numerical case study of a medical mask design showed that the proposed model could calculate the face-mask contact pressure efficiently (0.0448 sec per design). In a pilot usability experiment, the measured contact pressure was found similar values (range of mean contact pressure: 0.0093 ~ 0.0150 MPa) to the estimated values (range of mean contact pressure: 0.0097 ~ 0.0116 MPa).