In this paper, an approach based on the integration of computer-aided design and analysis (I-CAD-A) is used to develop new continuum-based finite element (FE) tire models for the small and large deformation analyses. Based on given tire specifications, the mechanics-based geometry/analysis absolute nodal coordinate formulation (ANCF) is used to define the tire geometry with the same degree of accuracy as B-splines and NURBS (Non-Uniform Rational B-Spline), widely used in the computer-aided design (CAD) systems. In the case of large deformations, the ANCF geometry can be used directly as the analysis mesh without the need for conversion or adjustments. In order to define the material parameters that characterize the ANCF tire composite structure, a virtual test rig is developed, and the tire calibration process is performed according to the standards defined by the Society of Automotive Engineers (SAE). In order to develop small-deformation models that can be used in the prediction of the tire frequencies and mode shapes, the ANCF position vector gradients are consistently written in terms of rotation parameters, leading to geometrically-accurate floating frame of reference (FFR) finite elements, referred to as ANCF/FFR elements. Using this mechanics-based geometry/analysis approach, new geometrically-accurate reduced-order tire models are systematically developed and used to define vibration equations for the prediction of the tire frequencies, which are verified using a commercial FE software.