An algorithm to estimate the shape of a flexible ultrasound array transducer from backscattered ultrasound signals is presented. The algorithm exploits the phase variation across the receive channels to compute an array shape focusing criterion related to the array shape. This metric quantifies the phase variation at a set of spatial positions and the correct array shape is identified by the maximum of this metric. Its practical implementation is presented in the context of an overall shape estimation workflow using both simulated and experimental data. Using a 128-element, 2.5 MHz centre frequency flexible array transducer, the channel data of a tissue-mimicking phantom were recorded. The beam response was calibrated with respect to a known array shape facilitating quick and accurate shape estimation from these data. The algorithm was demonstrated to accurately predict the array shape corresponding to a root mean square error of the estimated element locations within 0.18 $\lambda$ and 0.4 $\lambda$ using simulated and experimental data respectively. This was performed using data recorded from a single transmit event and in a calculation time of approximately 300 ms.