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A brief history of Monte Carlo methods is presented, with emphasis on uses in engineering. An overview of daylighting design is then presented, exploring both quantity and quality of light. Various strategies for achieving effectively daylit enclosures are examined, with heavy emphasis upon computation. Monte Carlo methods are the only ones which are sufficiently robust to handle specular surfaces and properties which vary with incident angle (such as for glass). A general purpose computer code, DAY3D, is developed and applied to the calculation of luminous intensities in general enclosures. Due to the requirement for huge computing resources, an architectural study of photon tracing on a Cray Y/MP and a CM-2 is performed, illustrating the promise of a small CM-2 architecture for this problem. Various strategies for visualizing both field results and the discrete Monte Carlo processes are explored.