Symbolic transducers are useful in the context of web security as they form the foundation for sanitization of potentially malicious data. We define Symbolic Tree Transducers as a generalization of Regular Transducers as finite state input-output tree automata with logical constraints over a parametric background theory. We examine key closure properties of Symbolic Tree Transducers and we develop a composition algorithm and an equivalence decision procedure for linear single-valued transducers.