This document proposes a cloud service selection model called CloudEval that evaluates non-functional properties and selects an optimal service based on both user-specified quality of service levels and goals. CloudEval uses grey relational analysis, a multi-attribute decision making technique, in the selection process. It considers attributes like availability, response time, price, reputation, performance, and financial credit from service level agreements. The model aims to address limitations of prior works that either focus on specific service types or require user involvement in evaluation.