Human tympanic membrane (or eardrum) is composed of three membrane layers with collagen fibers oriented in the radial and circumferential directions, and exhibits viscoelastic behavior with membrane (or in-plane) properties different from through-thickness (or out-of-plane) properties. Due to the interaction of bundled fibers and ground substance, which is inhomogeneous, these properties could change with locations. In this paper, we use nanoindentation techniques to measure the viscoelastic functions of four quadrants of tympanic membrane (TM). For measurement of in-plane Young's relaxation modulus we fixed a sectioned quadrant of the TM on a circular hole and used a spherical nanoindenter tip to apply force at the center of the suspended circular portion of the specimen. An inverse problem solving methodology was employed using finite element method to determine the average in-plane Young's relaxation modulus of the TM quadrant. Results indicate that the in-plane steady-state Young's relaxation modulus for four quadrants of the TM does not vary significantly. However, a variation of the modulus from 25.73 MPa to 37.8 MPa was observed with measurements from different individuals. For measurement of Young's relaxation modulus in the through-thickness direction a spherical indenter tip was used to indent into different locations on the surface of the TM specimen supported by a substrate. Viscoelastic contact mechanics analysis of the load-displacement curve, representative primarily of the through-thickness stiffness of the TM, was conducted to extract the Young's relaxation modulus in the out-of-plane direction. Results indicate a wide variation in steady-state Young's relaxation modulus, from 2 MPa to 15 MPa, in the through-thickness direction over the TM.