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We review current quantitative models of the biomechanics of bird sound production. A quantitative model of the vocal apparatus was proposed by Fletcher (1988). He represented the syrinx (i.e. the portions of the trachea and bronchi with labia and membranes) as a single membrane. This membrane acts as a valve that rapidly closes and opens during phonation. This model can be used as a basis to address comparative morphological and physiological questions. More recently, the syrinx was modelled as a simple modified oscillator. Many features of the sound were captured remarkably well. The parameter values, however, did not represent the distribution of the actual material properties of the syrinx. These models demonstrated the minimum number of parameters required to describe the essential dynamics of the sound signal. Furthermore, we address possible interesting future directions for modelling.