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This paper describes a three-dimensional (3-D) numerical model, first of its kind, for predicting the plasma behavior of high pressure (viz. high-intensity discharge (HID) and ultra high pressure) lamps. Two-dimensional (2-D) and axisymmetric plasma models are widely used as these are less complicated and fairly available. But 2-D and axisymmetric models are not useful for any lamp operation other than vertical burning. There are many systems where HID lamps are horizontally oriented and/or inclined. Therefore, a universal 3-D model is a must for the proper predictions of such lamp behavior. The developed plasma model solves the complete set of magnetohydrodynamic (MHD): transport equations of mass, momentum, and energy along, with the vector potential form of Maxwell's equations to account for the electromagnetic effects. Radiation of the energy balance is calculated using the P-1 radiation method by dividing the electromagnetic spectrum into several graybands. For presenting the model performance, calculations are done for a lamp having arbitrary geometry and operating conditions. The glass-bulb of the lamp is assumed ellipsoid and the interelectrode gap is taken as 5 mm. Although the model has the features of predicting properties of the whole domain (electrodes with nonequilibrium cathode-sheath, 3-D plasma region, 2-D glass bulb, and stems), we limit the presentation for the electrodes and plasma region only to control the article size. Operating conditions of the lamp are chosen as a direct current (dc) of 20 A, a discharge medium of Hg and Ar mixture, and an operating pressure of 0.11 MPa. Current levels of 30 and 40 A have also been used to predict the current effect on radiation output. Calculated plasma results show a clear deviation from axisymmetry for horizontal operation of the lamp. Temperature and other plasma fields are found as the strongest near the cathode tip. Effect of Lorentz forces on the plasma velocity is found very significant. For the case of 20 A, maximum temperature is found as about 11000 K and the maximum velocity as 6 m/s.