Two important beam combining errors, piston errors and tilt errors are studied. Supposing, both piston errors and tilt errors obey normal distribution with zero-mean but leaving standard deviations to be determined, according to Strehl ratio, the permitted maximal standard deviations of piston errors and tilt errors are calculated based on iterative algorithm, respectively. Relations between the permitted maximal standard deviations of the two beam combining errors and obscuration ratios and numbers of sub-telescopes are revealed. The permitted maximal standard deviations of piston errors have no relationship with obscuration ratios of the sub-telescopes; but they decrease slowly within a narrow range of 0.11λ～0.08λ as the numbers of sub-telescopes increase. In the case of known pupils size, the permitted maximal standard deviations of tilt errors decrease as the obscuration ratios of sub-telescopes increase, while they have no significant correlations with the numbers of sub-telescopes.