Measurement of motivation is important in determining the relative importance of behaviours to the animals in our care. Construction of demand functions based on operant conditioning techniques is one way to measure and quantify motivation of animals. In this particular study demand functions were used in an attempt to estimate the importance of resting in cattle. Furthermore, the sensitivity of the technique was determined by quantifying the effects of variations in the level of prior deprivation, and reward (lying) duration on elasticity and intensity of the demand function. Cows were housed in tether stalls where they could be deprived of lying by attaching a girth strap secured to a rafter above the animal. During a 3-h test period a panel was placed in front of each heifer and she could work by pressing this panel on fixed ratio schedules for a releasing mechanism to be activated allowing her to lie down. In experiment 1 the heifers were deprived of lying twice daily for either two periods of 3h or two periods of 6h prior to testing. The fixed ratio varied from 6 to 24 and the reward duration was 15 minutes. In experiment 2, heifers could lie for either 10 or 20 minutes per reward at either of the two deprivation levels used in experiment 1. Here the fixed ratio varied from 10 to 50. The demand functions were liner in arithmetic co-ordinates, which means that the elasticity may not be constant across fixed ratio values. In experiment 1, heifers earned more rewards higher the deprivation level. Heifers valued access to rest more after the longest deprivation. In experiment 2, the heifers earned more rewards after two periods of six hours of deprivation when a reward duration of 10 minutes was given than when reward duration of 20 minutes was given. The results of these experiments indicate that the longest reward duration was more valuable than the shortest when the deprivation prior to test was high. The variation in elasticity with prior deprivation and reward duration has to be considered in future studies of the demand for rest in dairy cattle.