Certain radiation treatments, such as conformal and intensity modulated treatments, involve isocentric treatment fields delivered using multiple angles or continuous angulation of the gantry, collimator and table. At our institution, treatments involving three angles (gantry, collimator, and table) can, if uncorrected, exhibit misalignments of 2 mm or more on premarked field centers and borders on the patient surface during the initial setup on a linear accelerator (linac), even though the linac operates within allowable mechanical tolerances. This paper is an analysis of three principal mechanical sources of patient alignment errors observed on linacs: (i) errors in table and gantry angle, (ii) displacement of gantry rotational axis during gantry rotation, and (iii) displacement between collimator and table rotational axes. On patient surfaces, these small, systematic mechanical errors can each be expected to produce misalignments of up to 1.5 mm, increasing to over 2 mm with nearly horizontal fields delivered at nonzero table angles onto highly oblique patient surfaces. For the underlying target volumes, the mechanical errors can, in combination, be expected to produce target volume misalignments of up to 1 mm on newly installed linacs and 3 mm on older linacs. Thus, 1 mm appears to be a mechanical limit on the positional precision of radiation treatments.