Until recently, laboratory testing of packaged systems has been undertaken by simulating vertical vibrations alone. However, with increasing demand for a reduction in packaging waste, the use lightweight systems, such as stretch film, is increasing. Such containment systems are susceptible to the lateral forces generated by the pitch and roll vibratory motion of vehicles due to road surface unevenness. If laboratory simulation is to be realistic, multi‐axial motion must be taken into account and an understanding of the relationships between the random heave, pitch, and roll vibrations is essential. This paper uses vibration data collected from a number of transport vehicles traveling along typical urban and suburban routes to establish the nature and level of the multi‐axial vibrations that exist. These are presented with average Power Density Spectra (PDS) as well as statistical distributions of the moving root‐mean‐square (rms). The paper analyses the data for correlation of the rms levels with respect to nonstationarity. This is important when simulating nonstationary (randomly fluctuating rms) vibrations for heave, pitch and roll. These statistical correlation functions are used to manage the relative rms levels of each of the three Degrees of Freedom (DoFs) when undertaking vibration simulations using multi‐axis vibration test systems. The results show that the relationships between the moving rms of heave, pitch and roll vibrations are not strongly correlated but can be characterized statistically as joint distributions to enable realistic simulation of multi‐axial random vibrations of road transport vehicles under controlled laboratory conditions.