Formal methods use a mathematically based notation to describe the specification of software system and, based on these they have a notation of an implementation satisfying a specification. Z notation has been widely used in academia and industry. One of the things that we have either to prove formally or to convince ourselves of in some other way, about every specification written in Z is that the initial state exists. This paper explores theoretically the test of initial states in Z specifications. The new concepts, constructed function and constrained states space are introduced. The testing approach proposed in this paper can be used to detect the erroneous initial state in Z specifications. By way of examples, the application of testing approach is given. Keywords: Z specifications, states space, constructed function, constrained states space.