Artificial institutions have been proposed to regulate the acting of the agents in open multi-agent systems (MAS). They are composed of abstractions such as norms, roles, goals, etc. In this paper, we say that an artificial institution is situated when the whole regulation that it performs is based on facts occurring in the environment where agents act. The conceiving of situated institutions is challenging as it requires to situate all abstractions possibly involved in the MAS regulation considering their different natures, semantics, life cycles, etc. This work introduces a conceptual model of a situated artificial institution (SAI), structured along two axes: norms and constitutive rules. While norms are based on status functions, the constitutive rules allow a SAI model to clearly state the conditions for an element of the environment to carry a status function. From a first version of a SAI specification language based on this conceptual model, we discuss its features and illustrate its dynamics through examples.