The paper examines the problems of the indexical reference and the semantics of the indexical expressions. The basis of its approach is David Kaplan’s theory of indexicals, according to which the meaning of the indexical expression is constituted by two units: one of them is constant – so called character of the indexical expression, the other is changeable – so called content of the indexical expression. The character of the indexical expression is a linguistic rule, by which we can find out the re-ferent of a given indexical expression in dependence on the context of its use. The content of the indexical expression uttered in a given situation context is constituted by its referent. From the perspective of semantics – which aim is to identify the truth condition of the statements, so called propositions – only the changeable unit, i.e. the content of the indexical expression enters the truth condition of the indexical statement. The indexical expressions uttered in different situation contexts may have different contents. Then it is important that if the indexical expression refers to the relevant object in one utterance concerning it – so that the indexical expression gets its content –, this indexical expression does not refer to any other object in any other logically possible world. It means that the indexical expression also gets its constant content by its utterance in a given situation context. That is why the indexical expressions are rigid designators.