Constrained microbubble dynamics and coupling with surrounding microvessels is an important area of research for ultrasound contrast agents. Understanding the dynamics requires knowledge of the microvessel mechanical properties. In the present work, studies of microbubble-induced deformation and relaxation were performed on microvessels in ex vivo rat mesenteries. A Voigt model of tissue (parallel spring and dashpot) was used to fit the experimental relaxation time constant τ. All the correlation coefficients of the Voigt model and the experimental data were larger than 0.8, indicating a strong fit. The estimated τ ranged from less than 5 μs to almost 60 μs. No significant difference was found in τ for microvessels with diameters ranging from 20-80 μm. The relaxation time constant is directly associated with the ratio of elasticity to viscosity. The measured ratio provides constraints to possible values for the elasticity and viscosity of the microvessels.