A foodstuff such as a sausage is sliced in a predetermined slicing direction into a succession of slices each having a respective width measured parallel to the slice direction. This succession of slices is then deposited on a support in a plurality of rows with the slices in each row offset from one another by a predetermined first distance and the rows offset from each other by a predetermined second distance. The width of the slices is continuously measured as they are cut and at least one of the distances is automatically varied in dependence on the measured width to produce a uniformly overlapping array of slices. In addition the machine can calculate the weight of a given slice by combining the width with the slice thickness and the slice density, and this weight can be divided into a desired weight to determine how many slices at the predetermined size are needed to make up the desired weight. A signal can indicate then when this weight is reached.