Purpose The implementation of high performance computing (HPC) in business (especially small and medium-sized enterprises) is accompanied with mistrust to a certain extent, which has imposed the need for building of digital trust (DTrust) among stakeholders. The purpose of the present paper is to find out the ways on how to build and maintain such trust. Design/methodology/approach Analysis and critical reflection on previous research dealing with phenomena of digital transformation (DT), HPC, corporate digital responsibility (CDR) and DTrust have enabled the authors to design their own conceptual model as the answer to the research questions of how, and in what way, CDR influences DTrust. Findings The authors have determined that the previous researches pointed to the existence of the correlation between CDR and DTrust although they did not elaborate on this explicitly. It was shown that the DT itself directly influences trust and sustainability. The indirect influence DT has via CDR was the task the authors undertook through designing a new conceptual model within whose frame the authors separately presented the influence of total CDR on DTrust as well as of the specific CDR dimensions on the particular dimensions of DTrust. Originality/value The authors tried to offer the conceptual model that exactly determines the relation of individual dimensions of the processed phenomena by analyzing theoretical and empirical researches carried out so far, and eo ipso shed more light on their mutual relation. The authors firmly believe that this paper offers a useful frame for further empirical researches.