Prescriptive process-based safety standards (e.g. EN 50128, DO-178B, etc.) incorporate best practices to be adopted to develop safety-critical systems or software. In some domains, compliance with the standards is required to get the certificate from the certification authorities. Thus, a well-defined interpretation of the processes to be adopted is essential for certification purposes. Currently, no satisfying means allows process engineers and safety managers to model and exchange safety-oriented processes. To overcome this limitation, this paper proposes S-TunExSPEM, an extension of Software & Systems Process Engineering Meta-Model 2.0 (SPEM 2.0) to allow users to specify safety-oriented processes for the development of safety-critical systems in the context of safety standards according to the required safety level. Moreover, to enable exchange for simulation, monitoring, execution purposes, S-TunExSPEM concepts are mapped onto XML Process Definition Language 2.2 (XPDL 2.2) concepts. Finally, a case-study from the avionics domain illustrates the usage and effectiveness of the proposed extension.