Background: The assessment of radiation dose is of great importance in the optimization process. It is crucial to develop strategies for dose estimation in developing countries in lack of dosimeters. Material and Method: The Entrance Skin Dose (ESD) of 731 patients was calculated using the Davies model. Eight radiological procedures: Chest PA and LAT, lumbar spine AP and LAT, pelvis AP and LAT, skull PA and LAT and three-phase X-ray machines were considered. Based on the mathematical estimation of the radiation output of X-ray machines, a modified Davies model was proposed. The model was compared to others (Edmonds, Tung and Tsai) using their Mean Relative Errors (MRE) with respect to the reference Davies model and the Student’s test of comparison of means. The 3^rd quartile values were also compared to those found in Cameroon, Nigeria, Iran, France and UK. Results:  The MRE of the proposed model in this work (1.9%) was significantly less than the MRE of the Tung and Tsai model (7.1%), which was in turn significantly less than the MRE of the Edmonds model (55.0%). Results also show that, the 3^rd quartile values were mostly higher than reference level in UK. High values of doses are attributable to short Focus to Skin Distance (FSD) and high values of charges. Conclusion: The model proposed in this study is a better alternative to the Davies model in the case of absence of dosimeter. An adjustment of technical parameters (FSD and charge) could help reduce high doses.