Two thin conducting, electrically neutral, parallel plates forming an
isolated system in vacuum exert attracting force on each other, whose origin is
the quantum electrodynamical interaction. This theoretical hypothesis, known as
Casimir effect, has been also confirmed experimentally. Despite long history of
the subject, no completely convincing theoretical analysis of this effect
appears in the literature. Here we discuss the effect (for the scalar field)
anew, on a revised physical and mathematical basis. Standard, but advanced
methods of relativistic quantum theory are used. No anomalous features of the
conventional approaches appear. The Casimir quantitative prediction for the
force is shown to constitute the leading asymptotic term, for large separation
of the plates, of the full, model-dependent expression.