This dissertation describes an investigation of modal analysis methods for the detection, location, and characterization of flaws or damage in a structure or machine. The type of damage considered in the research was restricted to narrow, rectangular slots in symmetric trapezoidal plates. Both modal testing and finite element methods were used to investigate changes in natural frequencies of a clamped trapezoidal plate for all combinations of three slot lengths and three slot orientations. For modal testing, an impulse hammer was used to excite plate vibration, and a near field microphone was used to measure the response of the test plates. The first five natural frequencies were estimated from the measured frequency response function. Modal shapes associated with the natural frequencies were determined roughly from the phase of the measured frequency response function. Natural frequencies and associated modal shapes were also estimated numerically using the ADINA finite element package. Changes in natural frequencies for four different slot widths were investigated using finite element analysis. The changes in natural frequencies obtained by the two methods were in good agreement for all cases studied, and the results agree well with previously published work for an undamaged plate;The investigation demonstrates that: (1) Slot presence can be detected from the change in natural frequency of the plate. (2) Slot length and angular orientation have significant effect on natural frequencies of the plate. (3) Slot width has no significant effect on natural frequencies of the plates. (4) Slot presence can change the numerical order of the natural frequencies associated with adjacent modes of the plate. (5) Slot presence has little influence on modal shapes;The results demonstrate that impact vibrational testing using a near field microphone as the response transducer is a viable method for macroscopic non-destructive evaluation.