This paper presents design considerations for vibration assisted compliant assembly involving peg-in-hole insertion. We propose a feasible parts mating assembly model, based on the positional uncertainty and tolerance of an assembly task. For an infeasible task, whose tolerance set does not contain the uncertainty set, it is proposed to introduce a relative motion between the two mating parts, so as to enlarge the task tolerance relative to its uncertainty. A specific type of such motion, viz vibration in two orthogonal directions, is studied in detail. The amplitudes and frequencies of vibrations are determined for given tolerance, uncertainty, and other assembly parameters. A numerical procedure is devised to select the ratio of the two orthogonal vibration frequencies, for minimum search time of parts engagement. Criteria on suitable compliances for assembly are proposed, with consideration of insertion failure.