The present paper refers to the numerical prediction of air velocities and temperatures inside single-sided naturally ventilated buildings and more specifically the special case in which air from the external environment is brought into the building through single-directed openings. The work is focused on the physical procedures governing air movement during the single-sided natural ventilation. The study presents a mathematical model, implemented in a general computer code, that can provide detailed information on velocity and temperature, prevailing in three-dimensional, single-sided ventilated buildings with openings of any geometrical complexity, for given external meteorological conditions. The mathematical model involves the partial differential equations governing flow and heat transfer in large enclosures. Turbulent flow is simulated and buoyancy effects are taken into account. The model is used to assess the environmental conditions in a test cell designed and constructed by the National Observatory of Athens with external conditions corresponding to their measurements. The numerical results are in good agreement with the experimental values of air velocity, temperature and pressure, at various sites inside the test cell,