Texture plays an important role in image analysis and understanding, with many applications in medical imaging and computer vision. However, analysis of texture by image processing is a rather difficult issue, with most techniques being oriented towards statistical analysis which may not have readily comprehensible perceptual correlates. We propose new methods for auditory display (AD) and sonification of (quasi-) periodic texture (where a basic texture element or `texton' is repeated over the image field) and random texture (which could be modeled as filtered or `spot' noise). Although the AD designed is not intended to be speech- like or musical, we draw analogies between the two types of texture mentioned above and voiced/unvoiced speech, and design a sonification algorithm which incorporates physical and perceptual concepts of texture and speech. More specifically, we present a method for AD of texture where the projections of the image at various angles (Radon transforms or integrals) are mapped to audible signals and played in sequence. In the case of random texture, the spectral envelopes of the projections are related to the filter spot characteristics, and convey the essential information for texture discrimination. In the case of periodic texture, the AD provides timber and pitch related to the texton and periodicity. In another procedure for sonification of periodic texture, we propose to first deconvolve the image using cepstral analysis to extract information about the texton and horizontal and vertical periodicities. The projections of individual textons at various angles are used to create a voiced-speech-like signal with each projection mapped to a basic wavelet, the horizontal period to pitch, and the vertical period to rhythm on a longer time scale. The sound pattern then consists of a serial, melody-like sonification of the patterns for each projection. We believe that our approaches provide the much-desired `natural' connection between the image data and the sounds generated. We have evaluated the sonification techniques with a number of synthetic textures. The sound patterns created have demonstrated the potential of the methods in distinguishing between different types of texture. We are investigating the application of these techniques to auditory analysis of texture in medical images such as magnetic resonance images.