A locating array is a mathematical object that is intended to be used for fault localization in combinatorial interaction testing. However, applying it to a real-world testing is difficult because a system under test often has constraints among test parameter values. Test cases must satisfy such constraints to be executed; but the definition of locating arrays does not consider constraints. Hence directly using a locating array as a test suite results in interactions that are not tested as well as faulty interactions that cannot be identified. In this paper, we propose a method of generating Constrained Locating Arrays (CLAs), which are a constraint-aware extension of locating arrays. The proposed method uses a Satisfiability Modulo Theories (SMT) solver to search for a CLA. Experimental results show that the proposed method is often fast enough to find a minimum CLA for a nontrivial case. % Locating arrays have been proved its effectiveness on fault detections in software testing. However it is impractical for industrial usage for most of the systems have constraint restrictions. All of such constraints that exist between parameters and functions need to be satisfied by any test case. In this paper, we propose an SMT-based generation method on constrained locating array, an extended locating array that takes account of constraints. Experimental results shows the lower bounds on the size of test suite for each system which also proves the method is efficient. And with the results, we give some advices on further generations.