Microbubbles are currently used as ultrasound contrast agents. Their potential therapeutic applications are also under investigation. This work is designed to provide some insight into the mechanisms of energy absorption and deposition by a preformed gas bubble in the microvasculature to optimize its efficacy. In the linear regime, the most favourable condition for the transfer of energy from an ultrasonic field to a gas bubble occurs when the centre frequency of the ultrasonic field equals the resonance frequency of the bubble. The resonance frequency of gas microbubbles has been investigated up to now mainly in unbounded liquids; however when bubbles are confined in small regions, their resonance frequency is strongly affected by the surrounding boundaries. A parametric study on how the resonance frequency of microbubbles in blood vessels is affected by the bubble radius, vessel radius and the bubble position in the vessel is presented. The resonance frequency decreases below its free value with decreasing vessel radius for vessels smaller than 200-300 microm depending on the bubble size. This model suggests the possibility of using ultrasound in a range of frequencies that are, in general, lower than the ones used now for therapeutic and diagnostic applications of ultrasound (a few MHz). When microbubbles oscillate at their resonance frequency they absorb and therefore emit more energy. This energy may allow specific blood vessels to be targeted for both diagnostic and therapeutic applications of ultrasound.