This paper describes MATA (Modeling Aspects Using a Transformation Approach), a UML aspect-oriented modeling (AOM) technique that uses graph transformations to specify and compose aspects. Graph transformations provide a unified approach for aspect modeling in that the methods presented here can be applied to any modeling language with a well-defined metamodel. This paper, however, focuses on UML class diagrams, sequence diagrams and state diagrams. MATA takes a different approach to AOM since there are no explicit joinpoints. Rather, any model element can be a joinpoint, and composition is a special case of model transformation. The graph transformation execution engine, AGG, is used in MATA to execute model compositions, and critical pair analysis is used to automatically detect structural interactions between different aspect models. MATA has been applied to a number of realistic case studies and is supported by a tool built on top of IBM Rational Software Modeler.