Abstract A new method to calculate mass-attenuation coefficients of β− and β+ particles of energies from 0.25 to 5.0 MeV for elemental absorbers is described. This method is based upon the interactions of β− and β+ particles with matter and the use of the varying transmission limit for different absorbers. The root-mean-square (r.m.s.) deviation of theory from 61 electron and 30 positron measurements in all elements is 6.5 and 9.7% respectively. Attenuation coefficients in rare earths calculated by this method are in excellent agreement with earlier measurements.