The components which often fail in a rolling element bearing are the outer-race, the inner-race, the rollers, and the cage. Such failures generate a series of impact vibrations in short time intervals, which occur at Bearing Characteristic Frequencies (BCF). Since BCF contain very little energy, and are usually overwhelmed by noise and higher levels of macro-structural vibrations, they are difficult to find in their frequency spectra when using the common technique of Fast Fourier Transforms (FFT). Therefore, Envelope Detection (ED) is always used with FFT to identify faults occurring at the BCF. However, the computation of ED is complicated, and requires expensive equipment and experienced operators to process. This, coupled with the incapacity of FFT to detect nonstationary signals, makes wavelet analysis a popular alternative for machine fault diagnosis. Wavelet analysis provides multi-resolution in time-frequency distribution for easier detection of abnormal vibration signals. From the results of extensive experiments performed in a series of motor-pump driven systems, the methods of wavelet analysis and FFT with ED are proven to be efficient in detecting some types of bearing faults. Since wavelet analysis can detect both periodic and nonperiodic signals, it allows the machine operator to more easily detect the remaining types of bearing faults which are impossible by the method of FFT with ED. Hence, wavelet analysis is a better fault diagnostic tool for the practice in maintenance.