To better understand the phase transition mechanism of PbZrO3 (PZO), the lattice dynamics of this antiferroelectric compound are investigated within the polarizability model, with emphasis on the cubic to orthorhombic phase transition. Similarly to ferroelectric phase transitions in ABO3 perovskites, polar dynamical clusters develop and grow in size upon approaching T(C) from the high temperature side and never form a homogeneous state. Simultaneously, elastic anomalies set in and compete with polar cluster dynamics. These unusual dynamics are responsible for precursor effects that drive the PZO lattice towards an incipient ferroelectric state. Comparison of the model calculations with the temperature dependences of elastic coefficients measured on PZO single crystals reveals a striking similarity.