Selective Harmonic Elimination (SHE) is an established technique to eliminate unwanted harmonics that causes aliasing effect in communication systems and affects power quality in electrical systems. In this paper, an analytical approach for SHE is proposed for harmonic elimination in a multilevel inverter. Traditionally, numerical methods like Newton Raphson Algorithm are opted to solve the transcendental SHE equations. The disadvantage in iterative computation is overhead in computational effort and the solution time can be problematic in real-time operation. Additionally, the numerical methods are sensitive to initial values and produce just one solution depending on the initial values. It doesn't provide insight into the possible solution sets. The closed-form equations generate the appropriate transition angles, single or multiples and the modulation ratio can be programmed into a microcontroller to vary the fundamental while eliminating the targeted harmonics. The approach has been illustrated to eliminate up to 7th harmonic in a seven level single phase inverter and up to 11th in a three phase system (no triplen harmonic elimination). Simulation results are included to verify theoretical formulation. A low voltage seven level inverter was built with a H-bridge and the experimental results verify the theoretical findings. Results include both single phase and triplen systems.