Ultra4 is an international racing series with races held in severe weather conditions on most demanding terrains of North America and Europe. The topics of this thesis is design of dependent suspension for an Ultra4 race vehicle, which includes 3 link front suspension and 4 link rear suspension. The introduction presents some general information about Ultra4 racing and most important rules for different vehicle classes. Next, a survey of dependent suspension types and suspension parts is made. Suspension will be designed in three different ways, in order of increasing complexity. The first suspension is designed based on general guidelines that are a result of years of racing experience. Mathematical formulas for design of dual rate coilover dampers are created, which account for all limiting factors and ensure that damper is functional through full suspension motion. The most important parameters for evaluation of dependent suspension are mathematically analysed using relevant vehicle dynamics and suspension sources. Based on that analysis, the second suspension is designed. A computer programm for calculation of solid axle suspension motion for axle bump and roll is created in programming language Python. Data calculated in kinematic analysis is used for creating Ultra4 vehicle model in software for vehicle dynamics simulation CarSim 8.1. The procedure for vehicle simulations includes a terrain full of irregularities, with severe inclinations and a low coefficient of friction to make it as similar as possible to real race courses. In the third design step suspension parameters are optimized using evolutionary algorithm. A Python program is written to connect CarSim to various optimization algorithms and to enable the automation of vehicle dynamics simulations. Based on optimization results, the third suspension is designed. All suspension designs are compared based on vehicle dynamics simulation results.