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Multibunch instabilities due to beam-coupling impedance can be a critical limitation for synchrotrons operating with many bunches. To study these instabilities, the HEADTAIL code has been extended to simulate the motion of many bunches under the action of wake fields. All the features already present in the single-bunch version of the code have remained available, in particular synchrotron motion, chromaticity, amplitude detuning due to octupoles and the ability to load any kind of wake fields through tables. The code has been then parallelized in order to track thousands of bunches in a reasonable amount of time, showing a linear scaling with the number of processors used. We show benchmarks against Laclare's theory in simple cases, obtaining a good agreement. Results for bunch trains in the LHC and comparison with beam-based measurements are also exhibited.
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