In this pandemic situation, importance and awareness about mental health are getting more attention. Stress recognition from multimodal sensor based physiological signals such as electroencephalogram (EEG) and electrocardiography (ECG) signals is a very cost-effective way due to its noninvasive nature. A dataset, recorded during the mental arithmetic task, consisting of EEG + ECG signals of 36 participants is used. It contains two categories of performance, namely, “Good” (nonstressed) and “Bad” (stressed) (Gupta et al. 2018 and Eraldeír et al. 2018). This paper presents an effective approach for the recognition of stress marker at frontal, temporal, central, and occipital lobes. It processes the multimodality physiological signals. The variational mode decomposition (VMD) strategy is used for data preprocessing and for the decomposition of signals into various oscillatory mode functions. Poincare plots (PP) are derived from the first eight variational modes and features from these plots have been extracted such as mean, area, and central tendency measure of the elliptical region. The statistical significance of the extracted features with p < 0.5 has been performed using the Wilcoxson test. The multilayer perceptron (MPLN) and Support Vector Machine (SVM) algorithms are used for the classification of stress and nonstress categories. MLPN has achieved the maximum accuracies of 100% for frontal and temporal lobes. The suggested method can be incorporated in noninvasive EEG signal processing based automated stress identification systems.