In the presented work, a model of a microelectromechanical accelerometer with two microbeam sensing elements located between two fixed electrodes is proposed. The action of the inertia forces in the longitudinal direction affects the spectral properties of the system. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of in-phase and anti-phase oscillations with small changes in the applied acceleration. Diagrams of equilibrium positions are obtained varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is concluded that the amplitude sensitivity of the proposed sensor is orders of magnitude higher than frequency shift sensitivity. Peculiarities of the sensor nonlinear dynamics is investigated in case of external harmonic electrostatic actuation. Principal difference in the characteristics of mode localization phenomenon is revealed between the linearized model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear effects.