Transporting sheep by sea exposes them to some prolonged floor motions, and their responses may depend on their space allowance. We simulated sea motion in a crate with a moveable and programmable floor, to measure behaviour and physiological responses. Nine sheep were exposed in groups of 3 for 1 h periods to Regular motion (8° roll of the floor every 15 s), Irregular motion (30 randomly selected amplitudes and duration of floor roll, with the same means as Regular), and No floor motion, at High (0.35m2/head), Medium (0.30 m2/head), and Low (0.26 m2/head) space allowances, with Low representing the Australian shipping standard. Lying time (P < 0.001) and heart rate (P = 0.05) were reduced during regular motion, but aggression increased during irregular motion (P < 0.001), particularly at the end of the treatment. Both regular and irregular motion decreased rumination (P = 0.003) compared with control. Pushing (P = 0.03) and stepping (P < 0.001) were more frequent in the Low than Medium or High space allowance treatments, but only when the sheep experienced Regular motion, and particularly at the start of treatment (P = 0.03, P < 0.001) respectively. Low space allowance decreased lying time (P = 0.001) and variability in cardiac interbeat intervals (P < 0.001), increased aggression (P = 0.005) and the time sheep had their head facing downwards resting on the bars of the cage (P = 0.02), indicating stress. Therefore, both regular and irregular ship-like motion at a low space allowance led to responses that suggested stress; giving more space than the current Australian standards may increase the welfare of sheep transported by sea.