We perform for the first time spectroscopic mode identification in the eclipsing binary beta Cephei star EN(16) Lac. This mode identification is based upon a time series of 942 line profiles of the He I lambdalambda6678 Angstrom line in its spectrum. All three known frequencies f(1); f(2); f(3) of the star are present in the line-profile variations, but we failed to find additional modes. Using different identification methods we find conclusive evidence for the radial nature of the main mode and for the l = 2; m = 0 identification of the mode with frequency f(2). A unique identification of the third mode is not possible from the spectra, but we do derive that l(3) < 3. Fits to the amplitude and phase variability of the modes imply a rotation frequency between 0.1 and 0.4 c d(-1). The star's rotation axis is not aligned with the orbital axis.