A method has been demonstrated in which the emission of characteristic X-rays following impact ionization by electrons of several MeV energy is used for quantitative elemental analysis. Because of the unique properties of MeV electrons with respect to their X-ray production yield and range in solids, the method has comparable sensitivity over a wide range of elements and relatively less stringent sample preparation requirements. By using energy dispersive techniques to detect the X-rays, a simultaneous determination of the weight fraction of the elements in an unknown sample is possible from a procedure based entirely on empirically determined relative X-ray yields. The method was tested by analyzing three standard metal alloy samples obtained from the National Bureau of Standards. Elements reaging from iron (Z=26) to lead (Z=82) with concentrations from 0.06% to 88% were quantitatively determined. In general, good approximate agreement was found wit the reported assays even for the minor constituents.