This paper explores the analysis and classification of speech under stress using a new feature, harmonic peak to energy ratio (HPER). The HPER feature is computed from the Fourier spectra of speech signal. The harmonic amplitudes are closely related to breathiness levels of speech. These breathiness levels may be different for different stress conditions. The statistical analysis shows that the proposed HPER feature is useful in characterization of various stress classes. Support Vector Machine (SVM) classifier with binary cascade strategy is used to evaluate the performance of the HPER feature using simulated stressed speech database (SSD). The performance results show that the HPER feature successfully characterizes different stress conditions. The performance of the HPER feature is compared with the mel frequency cepstral coefficients (MFCC), the Linear prediction coefficients (LPC) and the Teager-Energy-Operator (TEO) based Critical Band TEO Autocorrelation Envelope (TEO-CB-Auto-Env) features. The proposed HPER feature outperforms the MFCC, LPC and TEO-CB-Auto-Env features. The combination of the HPER feature with the MFCC feature further increases the system performance.