Aspect-Oriented Programming (AOP) provides new constructs and tools to handle cross-cutting concerns in programs. Fully realizing the potentials of Aspect-Oriented Software Development requires new abstractions and techniques for testing. This paper proposes a first step towards a practical approach to test aspect-oriented software. The proposed approach is accompanied by a selection algorithm that can select test cases that are relevant to aspects under test. A new testing coverage definition is proposed to specify the sufficiency of test cases on the aspect being tested. A tool is developed to support the approach, automating test case selection and coverage calculation. A detailed case study of banking account processing illustrates this initial approach.