Human tooth enamel possesses unique morphology characterized by repeated cell arrangement. Due to its complex structure, various investigators have reported diverse mechanical models and properties in their experimental and numerical studies. In this paper, the proper behavior described by the monoclinic model is reported and the effects of hydroxyapatite fibers and prism rods on the effective properties of tooth enamel are presented. The results are obtained from 3D finite element analysis with a novel procedure to construct periodic cell models and impose boundary conditions. This specialized approach allows determinations of 13 independent material constants needed for the monoclinic model. These constants may be used to construct homogenized models to study the mechanical behavior of entire tooth under abrasion, erosion, wear and fracture. In addition, a large scale 3D analysis was also performed to simulate instrumented micro-indentations of tooth enamel. The computed results are compared with experimentally obtained load-displacement measurements to verify the proposed model for the tooth enamel.