To analyse ultrasonic echoes from soft tissues a fast data acquisition system was built. A PDPS/E minicomputer controls a Biomation 8100 transient recorder and an RBBE disk storage unit. The transient recorder can digitise at sample rates up to 100 MHz, with a resolution of up to 8 bits. The design of the transient recorder interface is described, single cycle databreak transfers are used, and three 8-bit bytes of data can be packed into every two computer words. Maintenance facilities in the interface allow detailed testing. An assembly language program allows flexible acquisition of echo data. The transient recorder acquisition parameters may be specified by keyboard commands and stored onfile. Approaches to tissue characterisation are briefly reviewed. One fundamental problem is that interference between echoes from closely spaced scatterers introduces a random element in the echo amplitude. The problem of detecting an array of scatterers surrounded by a different array of scatterers is considered. Simulations based on a discrete scattering model aid the analysis. Signals are synthesised by adding echo pulses with random time delays. Distributions of the average-echo amplitude of synthesised data and liver echo data are compared. The detection of abnormal regions is discussed within the framework of statistical decision theory. The use of moving averages to detect abnormal regions is studied. Level crossing frequencies of various synthesised waveforms are compared with theoretical predictions. The random nature of echo amplitudes can limit the achievable resolution in standard B-scan images. Digital scan converter update algorithms are considered from a statistical viewpoint.