Propulsion systems are widely used to generate efective thrust for floating objects like ships, submarines and barges. A screw type propeller since it was developed has always been the most popular propulsion system due the simplicity, low maintenance cost and rotary driving type complying to the machinery. Given work is dedicated to reveal new, alternative propulsion systems with biomimetic design as well as new on principal 6 DOF mathematical model of a floating object with the impact of the surrounding environment. Offered systems are similar to fish tail and also use the same working principle. Dissertation holds research on propulsion system types, several propulsion systems comparison and findings in the field. Several tasks were drawn. Biomimetic propulsion systems with sub-carangiform and carangiform body ratios were developed, the models were optimized. Further, propulsion systems with a non-elastic fan were developed. Several excitation types were used – harmonic exciation and adaptive excitation. The mathematical models were simulated in program MathCAD where also the optimization takes place. A parameter optimization method with a floating parameter was developed for use with MatCAD. A method is offered for floating robot movement modeling by dividing the object in 2 subsystems: calculation of propulsive thrust from the propulsion device; calculating floating objects hull dynamics by the propulsive thrust. A propulsion system with variable active work surface area is offered as a method of increasing efficiency. Mathematical model with various excitation systems simulation was done using MathCAD. The propulsion system with the variable active work surface area is also specifically viewed as navigational system with the ability to change the thrust direction in the horizontal motion plane. A method of floating robot synthesis with variable active work surface area is given. Following research reveals a three dimensional 6 DOF floating object model with the impact of wind, current, waves and propulsive thrust. Appendix holds experimental results of air drag coefficient measured in a wind tunnel. The proposed propulsion systems and methods and can be used as a theoretical and practical reference for further research development.