The capacitive coupled wireless power transfer (CCWPT) operating at megahertz (MHz) frequency is broadly considered as the promising solution for low power biomedical implants. The class E power amplifier is attractive in MHz range wireless power transfer (WPT) applications due to zero voltage switching (ZVS) and zero voltage derivative switching (ZVDS) properties. The existing design of class E amplifier is investigated only for inductive resonant coupled (IRC) WPT systems; the modelling and optimization of the class E amplifier for CCWPT systems are not deliberated with load variation. Meanwhile, the variations in the coupling distance and load are common in real time applications, which could reduce the power amplifier (PA) efficiency. The purpose of this paper is to model and optimize the class E amplifier for CCWPT systems used in MHz range applications. The analytical model of PA parameters and efficiency are derived to determine the optimal operating conditions. Also, an inductive-capacitive-inductive (LCL) impedance matching network is designed for the robust operation of the PA, which improves the efficiency and maintains required impedance compression. The maximum efficiency of the proposed design reached up to 96.34% at 13.56 MHz and the experimental results are closely matched with the simulation.