The protein threading problem with profiles is known to be efficiently solvable using dynamic programming. In this paper, we consider a variant of the protein threading problem with profiles in which constraints on distances between residues are given. We prove that protein threading with profiles and constraints is NP-hard. Moreover, we show a strong hardness result on the approximation of an optimal threading satisfying all the constraints. On the other hand, we develop two practical algorithms: CLIQUETHREAD and BBDPTHREAD. CLIQUETHREAD reduces the threading problem to the maximum edge-weight clique problem, whereas BBDPTHREAD combines dynamic programming and branch-and-bound techniques. We perform computational experiments using protein structure data in PDB (Protein Data Bank) using simulated distance constraints. The results show that constraints are useful to improve the alignment accuracy of the target sequence and the template structure. Moreover, these results also show that BBDPTHREAD is in general faster than CLIQUETHREAD for larger size proteins whereas CLIQUETHREAD is useful if there does not exist a feasible threading.