Visualization is the process of making something perceptible to the mind or imagination. The techniques for producing visual imagery of volumetric data have advanced immensely during the last decades to a point where each produced image can include an overwhelming amount of information. An increasingly viable solution to the limitations of the human sense of visual perception is to make use of not only vision, but also additional senses. This thesis presents recent work on the development of principles and algorithms for generating representations of volumetric data through the sense of touch for the purpose of visualization. The primary idea introduced in this work is the concept of yielding constraints, that can be used to provide a continuous set of shapes as a representation of features of interest in various types of volumetric data. Some of the earlier identified standard human exploratory procedures can then be used which enables natural, intuitive and effective interaction with the data. The yielding constraints concept is introduced, and an algorithm based on haptic primitives is described, which forms a powerful yet versatile implementation of the yielding constraints. These methods are also extended to handle time-varying, moving and low quality data. A framework for multimodal visualization has been built on the presented methods, and this is used to demonstrate the applicability and versatility of the work through several example applications taken from different areas.