Speech production can be viewed as a filtering operation in which a sound source excites a vocal tract filter. The vocal tract is modeled as a chain of cylinders of varying cross-sectional area in linear prediction acoustic tube modeling. In this modeling the most common implementation assumes equal length of tube sections. Therefore, to model complex vocal tract shapes, a large number of tube sections are needed. This paper proposes a new vocal tract model with unfixed sectionlengths, which uses the reduced lattice filter for modeling the vocal tract. This model transforms the lattice filter to reduced structure and the Burg algorithm to modified version. When the conventional and the proposed models are implemented with the same order of linear prediction analysis, the proposed model can produce more accurate results than the conventional one. To implement a system within similar accuracy level, it may be possible to reduce the stages of the lattice filter structure. The proposed model produces the more similar vocal tract shape than the conventional one.