Measurements of global solar radiation and duration of bright sunshine for the Republic of Sudan have been presented. For this purpose, nine index stations spread all over Sudan are chosen. The brightness ratio n/N, to be defined later, ranges between 0.373 and 0.923. The results show huge resources of solar energy available in Sudan. The correlationships between the global solar radiation and bright sunshine duration for this vast country have been developed by performing regression analysis using three models, namely linear, exponential and power. Excellent correlations were obtained for all three models, but the power one was found very marginally superior over the others. This suggests that the linear relationship can still be used with a great degree of accuracy. The correlationships have also been used to estimate evaporation rates. Further, the Piche coefficients (Cp), defined as the ratios of estimated evaporation rates to Piche measurements, have been obtained and compared with those suggested by other investigators. A reasonably good agreement has been found.