Most of the metaheuristics can efficiently solve unconstrained problems; however, their performance may degenerate if the constraints are involved. This paper proposes two constraint handling approaches for an emerging metaheuristic of Cohort Intelligence (CI). More specifically CI with static penalty function approach (SCI) and CI with dynamic penalty function approach (DCI) are proposed. The approaches have been tested by solving several constrained test problems. The performance of the SCI and DCI have been compared with algorithms like GA, PSO, ABC, d-Ds. In addition, as well as three real world problems from mechanical engineering domain with improved solutions. The results were satisfactory and validated the applicability of CI methodology for solving real world problems.