This paper addresses interactive function-based shape modeling where relatively small formulas are used rather than thousands of polygons. Interactive modification of the function model with concurrent visualization of the respective polygonal mesh lets us provide both the interactivity and any required level of detail leading to photo-realistic appearance of the resulting shapes. We have proposed a rendering method capable of handling local shape modifications with any desired precision. Also, we have proposed a few methods, which let us accelerate the final function evaluation -- a common bottleneck for the function-based shape modeling. Finally, we describe applications of the interactive function-based shape modeling to photo-realistic virtual embossing and carving.