Bottom hole assemblies (BHA) of oil drilling engineering were simplified as simply supported beam, and parametric resonances of BHA in mud drilling and air drilling were studied. Lateral vibration of BHA, which was induced by bit/formation interaction, was described and reduced into Mathieu equation by means of separation of variables and Galerkin method. Modified strained parameter method was adopted in stability analysis. The parametric resonance zones expressed by weight on bit (WOB) are presented here. It is found that drilling method, speed of rotation (SOR), material properties, and length of compression drillstring all can influence parametric resonance zones. So unstable responses can be avoided by adjusting these parameters.