Electrostatically actuated microstructures are widely used in microelectromechanical systems (MEMS). Computational analysis of electrostatic MEMS requires a self-consistent solution of the interior elastic domain and the exterior electrostatic domain. This paper proposes an efficient approach to carry out the dynamic analysis of electrostatic MEMS structures. The approach employs a meshless Finite Cloud Method (FCM) to solve the interior mechanical domain of the structures and a scattered point Boundary Cloud Method (BCM) to solve the exterior electrostatic domain. Lagrangian descriptions are used in both mechanical and electrostatic analyses. The electrostatic forces and mechanical deformations are all computed on the undeformed configuration of the structures. The approach provides an efficient computational tool for dynamic analysis of electrostatic MEM devices.