The Hermite numerical interpolation method used to estimate and predict the radon and radium concentrations, from some of the experimental measurements made on the soil samples of the Bartella region in Iraq. The results obtained from deductible mathematical method were close to real experimental results. Predicted results are in the range of 80.04–4051.59 Bq/m3radon concentrations and 0.322–17.276 Bq/Kgradium concentrations corresponding to 200-10000 tracks of alpha particles. The maximum errors were less than 0.289 and 1.172 percent for radon and radium concentrations, respectively. The effects of radium and radon radiations estimated of soil in the studied area depend on its concentrations, a higher number of alpha particle tracks mean high radiation concentration, the high radiation will cause human health damage. The values are below 370 Bq/Kg the recommended radium concentration permissible values, by the Organization ащк Economic Cooperation and Development (OECD), the studied area is safe from hazards on health of radium and radon exposure from the soil