The attenuation of solar radiation by the atmosphere is caused by two simultaneous processes: (a) scattering by air molecules and by the atmospheric turbidity; and (b) absorption by O 3, H 2O and CO 2. Since the atmospheric turbidity is closely related to horizontal visibility, V (meteorological optical range), the terrestrial direct normal solar radiation can be expressed as: I bn =I on exp(−N s K s − K t V −N o K o −N c K c −N w K w )mƒ where I on is direct normal extraterrestrial solar radiation; N o, N s, N c, and N w are thickness of the ozone layer in precipitate cm, the total number of gas moles, the number of CO 2 moles and the number of H 2O moles in the vertical atmosphere column, respectively; V is visibility in km; K s, K t, are the Rayleigh and the modified turbidity scattering coefficients; K o, K c, K w are the absorption coefficients of ozone, carbon dioxide and water vapour, respectively; m is relative air mass; f is the empirical function for air mass correction. Based on experimental measurements of direct normal solar radiation at different locations: Murmansk (polar zone), St Petersburg, Moscow, Kharkov, Crimea (Russia and Ukraine), Kabul (Afghanistan), and Gaborone (Botswana), a new physical model to calculate all variables and coefficients involved in the above equation is proposed. The model is based on laws of spectroscopy, kinetic theory and thermodynamics. A special software to predict direct normal solar radiation is developed. Comparison of the model proposed with the experimental measurements of I bn showed that the accuracy of the direct normal solar radiation obtained with this program is within 5% of the experimental data. For countries where the meteorological conditions do not change very much the accuracy can be improved to 3%. The model can be used at any location from the Northern to the Southern Pole, with only meteorological input data (pressure, temperature, relative humidity and visibility).