The first demonstrations of terahertz imaging in biomedicine were made several years ago, but few data are available on the optical properties of human tissue at terahertz frequencies. A catalogue of these properties has been established to estimate variability and determine the practicality of proposed medical applications in terms of penetration depth, image contrast and reflection at boundaries. A pulsed terahertz imaging system with a useful bandwidth 0.5-2.5 THz was used. Local ethical committee approval was obtained. Transmission measurements were made through tissue slices of thickness 0.08 to 1 mm, including tooth enamel and dentine, cortical bone, skin, adipose tissue and striated muscle. The mean and standard deviation for refractive index and linear attenuation coefficient, both broadband and as a function of frequency, were calculated. The measurements were used in simple models of the transmission, reflection and propagation of terahertz radiation in potential medical applications. Refractive indices ranged from 1.5 ± 0.5 for adipose tissue to 3.06 ± 0.09 for tooth enamel. Significant differences (P<0.05) were found between the broadband refractive indices of a number of tissues. Terahertz radiation is strongly absorbed in tissue so reflection imaging, which has lower penetration requirements than transmission, shows promise for dental or dermatological applications.