Conventional methods of numerical mapping (geographical information systems, GIS) are used widely to convert surface and subsurface geological maps into digital two-dimensional (2D) space, which can still be simply identified with a sheet of paper. Digital polygons, polylines and points represent geological information on intersectional surfaces (e.g. the terrain surface), without relief in most cases. This does not seem much different from traditional mapping. In general, conventional digital mapping deals only with the new technology of data acquisition, storage, processing and visualization. As in traditional mapping, the third dimension, which is so important for geologists, still remains hidden to the ordinary reader; one must interpret and penetrate the 2D map to imagine and understand subsurface structures. Should we, however, employ the third dimension, or even the fourth, in digital geological mapping? The computational power of modern hardware gives us the possibility to store, manage and visualize the voluminous and complex data necessary to present the 3D geological space. Recent industrial development presenting new techniques of computer modelling of spatial geological objects and processes can and may be applied in standard geological mapping. A 3D geological map of Poland is presented as an example of a product of multidimensional computer-based cartography. The map is still in the developmental stage and techniques of model construction and visualization are refined using numerical methods. A relatively large area of interest covering several different regional geological units is included in this model and it creates new challenges in 3D map production. The map is based on existing interpretations—archival, analogue subsurface geological maps, mainly on horizontal-section maps with a depth interval from −500 to −5000 m a.s.l. Data from drill holes and cross-country geological sections are also used as input to the model. A system of manipulation and visualization of 3D geological maps is proposed. The following topics are presented in the paper as features of the system: inclusion of 3D in GIS used in geological mapping (various techniques of geological data representation, intuitive visualization to display the multiplied, interbedded 3D objects in a form suitable for human perception and interpretation), 3D volumes (techniques of construction and visualization of 3D digital objects representing geological formations defined on stratigraphy, lithostratigraphy or lithology only) and faults (techniques of modelling and visualization of discontinuous tectonic structures in 3D).