This paper focuses on the influence of noise and vibration on auscultation with a digital stethoscope. Two types of vibrations, namely inputs through the patient chest and disturbances from the physician, influence the auscultation signal. The goal of this work is to reduce the influence of disturbances from the physician on the stethoscope's digital signal without effectively reducing the coupling between the transducer and the patient's chest. A multi-DOF rigid body vibration model consisting of discrete connected components is developed for a digital stethoscope. The model is experimentally validated and its parameters identified by using a thorax simulator and vibration shaker. The introduction of vibration isolation so as to reduce the influence of physician noise on the transducer is then pursued. It is shown that directly introducing soft foam vibration isolation between the transducer and the rest of the stethoscope structure leads to a reduction in coupling with the patient's chest. On the other hand, if the vibration isolation is introduced between the heavy transducer housing above the transducer and the rest of the stethoscope, then vibration isolation from the physician is achieved with a much less reduction in patient coupling. Experimental results are presented to study the influence of the proposed design changes.