In Europe and indeed worldwide, the General Data Protection Regulation (GDPR) provides protection to individuals regarding their personal data in the face of new technological developments. GDPR is widely viewed as the benchmark for data protection and privacy regulations that harmonizes data privacy laws across Europe. Although the GDPR is highly beneficial to individuals, it presents significant challenges for organizations monitoring or storing personal information. Since there is currently no automated solution with broad industrial applicability, organizations have no choice but to carry out expensive manual audits to ensure GDPR compliance. In this paper, we present a complete GDPR UML model as a first step towards designing automated methods for checking GDPR compliance. Given that the practical application of the GDPR is influenced by national laws of the EU Member States, we suggest a two-tiered description of the GDPR, generic and specialized. In this paper, we provide (1) the GDPR conceptual model we developed with complete traceability from its classes to the GDPR, (2) a glossary to help understand the model, (3) the plain-English description of 35 compliance rules derived from GDPR along with their encoding in OCL, and (4) the set of 20 variations points derived from GDPR to specialize the generic model. We further present the challenges we faced in our modeling endeavor, the lessons we learned from it, and future directions for research.