[en] We present the multibunch tracking code mbtrack developed to simulate, in 6-dimensional phase space, single- and multibunch collective instabilities driven by short- and long-range wakefields in storage rings. Multiple bunches, each composed of a large number of macroparticles, are tracked, allowing simulation of both intra- and interbunch motions. Besides analytical impedance models, the code allows employment of numerical wake potentials computed with electromagnetic (EM) field solvers. The corresponding impedances are fitted to a number of known analytical functions and the coefficients obtained in the fit are used as an input to the code. mbtrack performs a dynamic treatment of long-range resistive-wall and harmonic cavity fields, which are likely to be the two major factors impacting multibunch collective motions in many present and future ring-based light sources. Furthermore, it is capable of simulating beam-ion interactions as well as transverse bunch-by-bunch feedback. We describe the physical effects considered in the code and their implementation, which makes use of parallel processing to significantly shorten the computation time. mbtrack is benchmarked against other codes and applied to the MAX IV 3 GeV ring as an example, where the importance of the interplay of various physical effects as well as coupling among different degrees of freedom is demonstrated. - Highlights: • A new 6D multibunch multiparticle tracking code is developed. • The code employs numerical impedance computed for realistic vacuum components. • Effects of passive harmonic cavity and resistive wall are treated. • A method to model interplay between intra- and interbunch motions is developed.