Post-processing of multiple and hybrid finite element field solutions requires a post-processor that is more general than standard available tools. A novel three-level hierarchic post-processor structure is proposed. The first level of the post-processing environment is a library of programming objects representing mathematical entities such as fields, tables, geometries, meshes and numbers and of operations manipulating them. Frequently used post-processing tasks may be coded explicitly in this kernel and compiled into executable code. An interpreter for mathematical expressions forms the second level of the post-processor structure, Characteristic sequences of operations can be gathered in scripts or in functions and interpreted at run-time. The third level passes commands to the field parser or to the visualization routines. Selected simulation examples demonstrate the capabilities of the chosen approach.