Effect of anisotropy on the free and forced vibration behavior of hollow cylinders under dynamic internal pressure is investigated. The material is assumed to be cylindrically orthotropic. Laplace transform method is used and the inversion into the time domain is performed exactly using calculus of residues. Complex Laplace parameter in the free vibration equation has directly given natural frequencies and the results are listed in tabular form. On the inner surface various axisymmetric dynamic pressures are applied and hoop stresses are presented in the form of graphs for different values of an anisotropy parameter and wall thickness. The anisotropy parameter which essentially indicates the degree of anisotropy is the square root of a modulus ratio defined as the ratio of circumferential modulus to radial modulus. Increasing the anisotropy parameter provides a stress-amplification effect for thick-walled cylinders. Closed-form solutions obtained in the present paper are tractable and they allow for further parametric studies. The anisotropy constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution. The numerical values used are chosen arbitrarily and do not necessarily represent a certain material (C) 2009 Elsevier Ltd. All rights reserved.