We are investigating the utility of a new ultrasonic tissue characterization technique, specifically two-dimensional (2-D) spectrum analysis of radio-frequency backscatter signals, which promises to provide quantitative measures of the physical properties of tissue microstructures. Previously successful 1-D spectrum analysis is expanded to 2-D to more fully characterize diagnostically significant features of biological tissue. Two new spectral functions, radially integrated spectral power (RISP) and angularly integrated spectral power (AISP), are defined to quantitatively characterize tissue properties. This new approach is applied to the diagnosis of in vivo ocular melanomas. Our initial results indicate that 2-D spectrum analysis can provide significant new information on tissue anisotropy that are not apparent in 1-D spectra. Acoustic scattering models are applied to relate the 2-D spectral parameters to the physical properties (e.g., size and shape) of biological tissues.