Introduced in this (shortened) paper is a graphical modelling language for specifying concurrency in software designs. The language notations are derived from CSP and the resulting designs form CSP diagrams. The notations reflect both data-flow and control-flow aspects of concurrent software architectures. These designs can automatically be described by CSP algebraic expressions that can be used for formal analysis. The designer does not have to be aware of the underlying mathematics. The techniques and rules presented provide guidance to the development of concurrent software architectures. One can detect and reason about compositional conflicts (errors in design), potential deadlocks (errors at run-time), and priority inversion problems (performance burden) at a high level of abstraction. The CSP diagram collaborates with objectoriented modelling languages and structured methods.