This work investigates properties of the thin film elongation acoustic resonator (TFEAR) operating at megahertz frequencies in air. This resonator is composed of a piezoelectric layer of AlN sandwiched between 2 Al electrodes. TFEAR works in the extensional mode excited via AlN d31 piezoelectric coefficient. A 3D finite element method (3D-FEM) analysis using ANSYS software has been performed to model static modal and harmonic behavior of the TFEAR. To consider insertion losses into the substrate, equivalent electrical models based on a modified Butterworth-Van Dyke (MBVD) circuit have been improved by adding extra dissipative elements. Thus, a whole model for the on-wafer characterization setup is given, allowing for automatic de-embedding of the present TFEAR equivalent circuit. Quality factors Q as high as 2500 in air have been recorded with motional resistance lower than 400 ohms. A first oscillator based on a TFEAR resonator was also designed and tested.