<p><b>Abstract</b>—We consider the problem of embedding and reconfiguring binary tree structures in faulty hypercubes. We assume that the number of faulty nodes is at most (<it>n</it>−<it>2</it>), where <it>n</it> is the number of dimensions of the hypercube; we further assume that the location of faulty nodes are known. Our embedding techniques are based on a key concept called free dimension, which can be used to partition a cube into subcubes such that each subcube contains at most one faulty node. Using this approach, two distributed schemes are provided for embedding and reconfiguration in faulty hypercubes. We extend the free dimension concept to <it>degree of occupancy</it> and use this to develop a distributed scheme for reconfiguration of binary tree in faulty hypercubes with up to <tmath>$\lceil\, 3n/2\, \rceil$</tmath> node faults.</p>