This paper presents a novel blood pressure (BP) estimation method based on pulse transit time (PTT) and pulse arrival time (PAT) to estimate the systolic blood pressure (SBP) and diastolic blood pressure (DBP). A data acquisition hardware is designed for high-resolution sampling of phonocardiogram (PCG), photoplethysmogram (PPG) and electrocardiogram (ECG). PCG and ECG perform as the proximal timing reference to obtain PTT and PAT indexes, respectively. In order to derive a BP estimator model, a calibration procedure including a supervised physical exercise is conducted for each individual which causes changes in their BP and then, a number of reference BPs are measured alongside the acquisition of the signals per subject. It is suggested to use a force-sensing resistor (FSR) that is placed under the cuff of the BP reference device to mark the exact moments of reference BP measurements, which are corresponding to the inflation of the cuff. Additionally, a novel BP estimator nonlinear model, based on the theory of elastic tubes, is introduced to estimate the BP using PTT/PAT values precisely. The proposed method is evaluated on 32 subjects. Using the PTT index, the correlation coefficients for SBP and DBP estimation are 0.89 and 0.84, respectively. Using the PAT index, the correlation coefficients for SBP and DBP estimation are 0.95 and 0.84, respectively. The results show that the proposed method, exploiting the introduced nonlinear model with the use of PAT index or PTT index, provides a reliable estimation of SBP and DBP.Index Terms-cuff-less blood pressure, mobile health (mHealth), pulse transit time (PTT), pulse arrival time (PAT), vital signals