The article reveals opportunities and obstacles for cross-domain and cross-cultural knowledge transfer. Both interfaces are clearly present in biomimetics (the engineering branch that borrows ideas from biological field for introducing them into the technology). Biomimetic methodology needs to deal with key differences between domains (biology studies Life, engineering creates machines) and cultures (science describes and models, while engineering prescribes and produces). Due to the complexity of mentioned methodological issues biomimetics still remains case-study-based discipline with no guaranteed success of investments. Current paper offers the detailed explanation and procedures for biomimetic design. Authors discuss obvious and reveal invisible obstacles for mimicking living systems and the specifics of application of different TRIZ tools in cross-cultural and cross-domain knowledge transfers and present the algorithm for biomimetic engineering based on TRIZ.As a conclusion the list of axioms for biomimetic design is presented and the procedures for biomimetic design based on such axioms are suggested.