A binaural beat can be produced by presenting two tones of differing frequency, one to each ear. Such auditory stimulation has been suggested to influence behaviour and cognition via the process of cortical entrainment. However, research so far has only shown frequency following responses in the traditional EEG frequency ranges of delta, theta and gamma. Hence a primary aim of this research was to ascertain whether it would be possible to produce clear changes in the EEG in either the alpha or beta frequency ranges. Such changes, if possible, would have a number of important implications as well as potential applications. A secondary goal was to track any observable changes in EEG throughout the entrainment epoch to gain some insight into the nature of the entrainment effects any changes in an effort to identify more effective entrainment regimes. Twenty two healthy participants were recruited and randomly allocated to one of two groups, each of which was exposed to a distinct binaural beat frequency for ten 1-minute epochs. The first group listened to an alpha binaural beat of 10Hz and the second to a beta binaural beat of 20Hz. EEG was recorded from the left and right temporal regions during pre-exposure baselines, stimulus exposure epochs and post-exposure baselines. Analysis of changes in broad-band and narrow-band amplitude, and frequency showed no effect of either binaural beat frequency eliciting a frequency following effect in the EEG. Possible mediating factors are discussed and a number of recommendations are made regarding future studies, exploring entrainment effects from binaural beat presentation.