This paper presents an analytical model for the microendmill dynamics, including the setup errors, the axial force, the sectioned tool geometry, and the actual crosssection of the twisted fluted section. Different tool geometries and tool-grinding errors can also be incorporated in the presented model. To include the shear deformations and rotary inertia effects arising from the stubby nature of the microendmill, the Timoshenko beam equations are used in the derivation. The boundary-value problem is derived for each of the shank, taper, and fluted sections of the microendmill, and a component mode synthesis technique is used to combine the individual sections. A new spectral-Tchebychev technique is utilized to obtain the numerical solution of the boundary-value problem without resorting to the finite-elements technique. As a result, a simple yet accurate description of the microendmill dynamics is obtained. The solution is experimentally validated in Part II of the paper.