A machine (M) and a method for arranging objects (T, T1, T2) comprising a first end (Te) and a projecting edge (Tb) arranged in proximity to the first end, in an alternate manner along single file rows (F). The objects are oriented so that they rest on the first end and are divided into a first group (A) and a second group (B). The first group are moved in an anti-clockwise direction along a first arc of circumference (C1) and, simultaneously, the second group are moved in a clockwise direction along a second arc of circumference (C2). The objects (T1) of the first group and the objects (T2) of the second group are dropped in turn along the same direction (Y). The objects (T, T1, T2) are stacked on top of one another in an alternate manner along single file rows (F).