We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique (Navrátil et al. in J Phys G 36:083101, 2009) which we successfully applied in first calculations of the lightest Λ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon–nucleon and nucleon–hyperon interactions [such as those derived from EFT (Polinder et al. in Nucl Phys A 779:244, 2006)]. We discuss formal aspects of the methodology, show first demonstrative results for _Λ ³ H, _Λ ⁴ H and ⁴ _Λ He, and give outlook.