The problem of cross-cultural complexities is a hindrance to effective multicultural team leadership across many industries. Cultural differences among project team members cause conflict, misunderstanding, and poor project performance. The absence of competent leaders is a problem because business in the future will rely increasingly on the use of multicultural project teams. The purpose of this qualitative exploratory case study was to explore the challenges faced and the cultural competencies needed by project managers leading multicultural software development project teams to successfully manage and resolve cross-cultural interpersonal conflict amongst project team members. The researcher collected data using semi-structured interviews with the population of 12 project managers recruited from the Project Management Institute’s credentialed project management professionals LinkedIn group. Through a cross-case synthesis, the researcher identified common themes and aligned them with the two study constructs: cross-cultural interpersonal conflict resolution and multicultural skills. The findings of the research revealed that the project managers perceived challenges including language barriers, cycles of mistrust, and competitive attitudes when managing multicultural teams. In order to mitigate these difficulties, the participants reported that project managers require excellent communication, negotiation, and emotional intelligence skills. The contributions of this study to the field of conflict analysis and resolution include highlighting common cross-cultural complexities encountered in multicultural teams, as well as effective methods of minimizing, eliminating, or mitigating these issues and the resulting interpersonal conflict.