In this paper, we introduce a constraint-based reasoning approach to automatically generate test input for Java bytecode programs. Our goal-oriented method aims at building an input state of the Java Virtual Machine (JVM) that can drive program execution towards a given location within the bytecode. An innovative aspect of the method is the definition of a constraint model for each bytecode that allows backward exploration of the bytecode program, and permits to solve complex constraints over the memory shape (e.g., p == p.next enforces the creation of a cyclic data structure referenced by p). We implemented this constraint-based approach in a prototype tool called JAUT, that can generate input states for programs written in a subset of JVM including integers and references, dynamic-allocated structures, objects inheritance and polymorphism by virtual method call, conditional and backward jumps. Experimental results show that JAUT generate test input for executing locations not reached by other state-of-the-art code-based test input generators such as jCUTE, JTEST and Pex.