Detection of abnormalities in subcutaneous tissue is an important issue in medical diagnosis. Surgeons palpate this type of tissue to perceive pathologies through haptic sensation. This paper presents the framework of a real-time haptic-palpation system with inclusion detection to manipulate biological soft tissues and perceive their structures and material properties non-invasively. A user with a haptic device guides a robotic manipulator to perform palpation tasks and can detect the location of inclusions inside a soft medium (silicone-molded tissue phantom). For the objective measurement of the depth of the inclusion, a finite element (FE) model was developed to predict the reaction forces for various inclusion depths. The methods presented in this paper can be applied to the early detection of prostate cancer or breast cancer in telediagnosis.