This research aims to investigate the effects of some parameters on the nonlinear dynamics of an encapsulated microbubble. In the present study, the radial behavior of an encapsulated microbubble with modified Rayleigh-Plesset equation presented by Marmottant, van der Meer, Emmer, Versluis, de Jong, Hilgenfeldt, and Lohse [J. Acoust. Soc. Am. 118(6), 3499-3505 (2005)] is solved with matlab programming software. Radial dynamics of an individual microbubble for a free and coated state and effects of the added shell are also investigated. Results show that dilatational interfacial viscosity ( ks) of the shell and changes of surface tension have significant effects on the amplitude of oscillations, bubble dynamics, and bubble surface velocity. Regarding the fact that the velocity of the bubble surface has a significant role in stability and collapse of the bubble, it can be noted that this velocity is reduced considerably by adding the shell. Because of extensive usage of nonlinear microbubble oscillations in medical imaging techniques, the nonlinear response of a lipid-coated contrast agent called "compression-only" behavior is studied and effective parameters on this behavior are investigated. The results of bubble radius excursion reveal the fact that excitation frequency, pressure, and dilatational interfacial viscosity of the bubble affect the compression-only behavior.