Recently, there is an increasing interest in controlled excavation processes. However, the main attention, in research works, is paid to the bucket motion. This part of the process can be considered as a quasi static, kinematically induces process 8. It means that dynamic effects, by dropping accelerations terms can be neglected. This is not a case in the second part of the process consisting of: lifting the bucket filled with the soil, swinging the whole excavator with respect to vertical axis, lowering the bucket and discharging it. Next, the bucket is brought back to the excavation place again. Discussing these motions, one has to taking in to account dynamic effects. It should be also noted that mentioned motions are lasting approximately the same time as the digging process. It is then worthy to try to minimize the time needed for bringing the filled bucket to the discharge place, and back to the digging site. It is then the aim of the paper to present an optimal control of such a minimum time process. The paper deals with an optimum problem of positioning an excavator bucket along prescribed trajectory using minimum time. The paper is illustrated with numerical results giving some optimal trajectories.