Some works have already studied human trajectories during spontaneous locomotion. However, this topic has not been thoroughly studied in the context of human-human interactions, especially during collaborative carriage tasks. Thus, this manuscript aims to provide a broad analysis of the kinematics of two subjects carrying a table. In the present study, 20 pairs of subjects moved a table to 9 different goal positions distant of 2.7-5.4 m. This was performed with only one or both subjects knowing the target location. The analysis of the collected data demonstrated that there is no shared strategy implemented by all the pairs to move the table around. We observed a great variability in the pairs' behaviours. Even the same pair can implement various strategies to move a table to the same goal position. Moreover, a model of the trajectories adopted by collaborating pairs was proposed and optimized with an inverse optimal control scheme. Even if it produced consistent results, due to the great variability which origins were not elucidated, it was not possible to accurately simulate the average trajectories nor the individual ones. Thus, the approach that was shown to be efficient to simulate single walking subjects failed to model the behaviour of collaborating pairs.