After the space race to the Moon, Mars has been chosen the new destination to be explored by mankind. Cryogenic propellant is necessary to make space beyond the Moon accessible. Boil-off of cryogenic liquids raises the initial mass of spacecraft by increasing the amount of propellant required to carry-on. Therefore, mitigation of boil-off is key in reducing the mass of the propellant tank. The goal of the thesis is to find the mass optimum of a cryogenic propellant tank by varying the different passive and active insulation options. The question what the most mass efficient configuration of propellant and structure of a given cryogenic propellant tank for space applications using active and passive boil-off mitigation options is answered. Different options to reduce the heat flow to the fluid and vapour are identified. Spray-on foam insulation, multi-layer insulation and coatings are passive methods to prevent propellant from heating. An active component such as a cryocooler can be included in propellant tank design to remove heat from a system. It is also possible to increase the maximum allowable pressure, thereby increasing the saturation temperature of the liquid, or to reduce the initial storage temperature of the propellant to increase the heat capacity of a liquid before the liquid boils. A tool is developed which analyses different propellant tank design options by calculating the heat flow through the propellant tank insulation and structure to the fluid bulks. The propellant tank structure is divided into separate nodes and the heat flow between different nodes is calculated. The liquid and vapour bulks are also modelled as two nodes of the system. Heat is transferred between these nodes by radiation, conduction or convection. By analysing many options in a Monte Carlo-like system, a design optimised for the total mass can be selected. The Boil-off Monte Carlo program developed has models for different insulation methods. The conduction equation is used to identify the heat flow through the spray-on foam insulation and the propellant tank shell. For the multi-layer insulation, the empirical modified Lockheed equation is used to determine the heat flow over the layers of insulation. The mass penalty and power required for including a cryocooler to the design are found by using the empirical Ter-Brake and Air-force Laboratory relations for existing cryocoolers. In the mass penalty for the cryocooler, the additional mass for the power system and wiring are included. Different parts of the program have been verified. Due to a lack of experimental and flight data of existing spacecraft, the Boil-off Monte Carlo program is not validated. Two cases are analysed, a propellant depot orbiting Earth at geostationary orbit and the Centaur upper stage loitering to Mars. For the propellant depot, three mission duration are used to identify when passive-only insulation suffices and from when onward an active component saves mass. The Centaur upper stage mission is used to identify whether the stage can be used for a long space mission by only modifying the insulation. From the results, it can be concluded that it is most efficient to insulate a propellant tank with passive insulation if the mission duration is under a year. For a mission duration longer than 12 months, active measures reduce the mass of the tank compared to passive-only insulated designs. The Centaur stage can be used for longer space missions by adding MLI to the existing design. By adding a cryocooler boil-off can be mitigated for any mission. The most mass efficient configuration of the Centaur travelling to Mars is by adding 60 layers of MLI and a cryocooler providing 5 [W] of cooling power to the original design.