The article represents the application of swarm and evolutionary method of design of three different types of digital linear phase multiband stop filters (LPMBSFs). Two proposed meta-heuristic hybrid algorithms called cuckoo search particle swarm optimization (CSPSO) and improved CSPSO (ICSPSO) algorithms are employed for the successful design of these LPMBSFs. The proposed ICSPSO algorithm is developed combining the advantage of cuckoo search algorithm into particle swarm optimization (PSO) and its group searching capability is enhanced, tuning the mutation operator of differential evolution (DE) algorithm.