A computer aided adiabatic, non-isothermal plug flow reactor was designed for the Non-Catalytic Partial Oxidation of methane to Synthesis gas. Design equations for determining the functional dimensions and parameters of the reactor were developed and used to develop the design package for the reactor. The design equations were solved using MathLab and simulated with SimuLink 7.5 to determine optimum values/range of the functional parameters. The optimum values obtained were used to run the design program for a hypothetical reactor processing 600mmscf per day of natural gas. Simulation results showed that the functional parameters: space time and yield of products increases with increase in methane fractional conversion, while space velocity and selectivity decreases. Operating at high pressure (60 -70)bar, increases the selectivity of partial methane oxidation reaction, molar flow rate of synthesis gas (desired product) and space velocity, but decreases space time and reactor length required for high methane fractional conversion (0.95 - 0.99). For optimal functional parameters: feed inlet temperature of 1473K (1200oC), reactor diameter of 0.2m, total pressure of 60bar and methane fractional conversion of 0.95; the design program gave the reactor functional dimensions and parameters as:: Reactor volume = 0.1308m3, Reactor length = 9.7734m, Space time = 2.89E-07hr, Space Velocity = 0.2667hr-1, Yield of synthesis gas = 0.8578, Yield of carbon dioxide = 0.0922, Outlet Temperature = 1762.828 K. Keywords: Partial oxidation, Non-catalytic, Methane, Syngas, Reactor desig