One of the most important features of separation between benign or malignant tissues is their smooth or rough shape. This article presents a new method for early diagnosis of thyroid cancer by knowing the resonance frequencies of a certain tissue. Two types of nodules were investigated: spherical and elliptical. Their external surfaces were smooth or rough with different values of spicules. Propagation of sound through the human body was modeled by a classical partial differential equation associated with Neumann or Dirichlet boundary conditions. The assessments of about ten acoustic eigenfrequencies are enough to decide the type of external surfaces: smooth or rough, or whether nodule is benign or malignant. Data obtained by this method refers to the result of investigating 3D bodies smaller than 5 mm, when other medical devices such as ultrasound or CT cannot evaluate their surface shape because of their limited spatial resolution.