The availability of recently developed microelectromechanical system (MEMS) micro-mirror technology provides an opportunity to replace macroscale actuators for free-space laser beam steering in light detection and ranging and communication systems. Precision modeling of mirror pointing and its dynamics are critical to the design and control of MEMS beam steerers. Beginning with Hornbeck's torque approach, we present a first-principles, analytically closed-form torque model for an electrostatically actuated two-axis (tip-tilt) MEMS mirror structure. The torque expression is a function of the mirror's physical parameters, such as angles, voltages, and size. An Euler dynamic equation formulation describes the gimballed motion as a pair of damped harmonic oscillators with a coupled torsion function. Static physical parameters such as MEMS mirror dimensions and voltages are inputs to the model as well as dynamic harmonic oscillator parameters, such as damping and restoring constants, which are calculated or fitted to measurements. A Taylor series expansion of the torque function provides insights into MEMS behavior, including operational sensitivities near "pull-in." MATLAB and SIMULINK simulations illustrate performance sensitivities, controllability, physical limitations, and other important considerations in the design of precise pointing systems. Commercial-off-the-shelf micromirror measurements confirm the model's validity in steady state and dynamic scanning operations.