The purpose of this study is to construct a new three-dimensional vocal tract model that consider acoustical interactions between the vocal tract and the nasal cavity for advanced speech processing. To construct the model, three-dimensional shapes of the vocal tract and the nasal cavity of 10 adult males are measured in the steady state production of Japanese vowels using the magnetic resonance imaging technique. Measurement time is 15 second for a mid-sagittal section of the vocal tract, is 184 second for 20 axial sections from the larynx to the nasal cavity at a 6 mm interval, and is 184 second for 20 coronal sections from the tip of the nose to the atlas at a 5 mm interval. A computer algorithm for boundary tracing of the vocal tract and the nasal cavity from the MR images is proposed. The algorithm is based on the threshold operation. Thresholds of the gray level are computed from gray levels at border points of the vocal tract or the nasal cavity. Three-dimensional shapes of the vocal tract and the nasal cavity are obtained from the MR images using the present algorithm. The validity of the present algorithm is confirmed by the comparison the profile obtained by the algorithm with the original MR images.