The current standard technique for blood pressure determination is to use cuff/stethoscope, which is not suited for infants or children. Even for adults this approach yields 60% accuracy with respect to intra-arterial blood pressure measurements. Moreover, it does not allow for a continuous monitoring of blood pressures over the course of 24 h and even days. In this paper, a new methodology is developed that will enable one to estimate systolic and diastolic blood pressures based on the heart sounds measured directly from a human body. To this end, we must extract and separate the aortic, pulmonic, mitral, and tricuspid sounds that are involved in the first and second hear sounds, respectively, from the directly measured signals. Since many parameters such as the locations from which heart sounds are originated, and speed at which heart sounds travel inside a human body are unknown a priori, it is impossible to develop an analytic model to determine the blood pressure. Hence, an empirical model is developed to estimate blood pressures based on the data measured by two sensors. Preliminary clinical tests show that the methodology can separate heart sounds and estimated systolic and diastolic blood pressures correlate well with the benchmark data.