Gantry robots are mainly employed for applications requiring large workspace, with limited higher manipulability in one direction than the others. The Gantries offer very good mechanical stiffness and constant positioning accuracy, but low dexterity. Common gantries are CNC machines with three translational joints XYZ (3DOF) and usually with an attached wrist (+3DOF). The translational joints are used to move the tool in any position in the 3D workspace. The wrist is used to orient the tool by rotation about X, Y and Z axis. This standard kinematic structure (3T3R) produces a rectangular workspace.In this paper a full kinematic model for a 6DOF general CNC (gantry) machine is presented, along with the Jacobian matrix and singularity analysis. Using Denavit-Hartenberg convention, firstly, the general kinematic structure is presented, in order to assign frames at each link. The forward kinematic problem is solved using Maple 17 software. Differential kinematics describes the analytical relationship between the joint motion and the end-effector motion in terms of velocities, through the manipulator Jacobian matrix. The configuration at which the manipulator Jacobian matrix drops rank is called singular configuration. In this paper the Jacobian matrix is derived using the vector cross multiplication method. The singularity conditions are examined and validated. The fully reachable workspace is plotted with Matlab tools using specified joint limits.The presented solutions are expressed in parametric manner and can be used for analysis of the existing gantry type machine as well as a design tool for new machines.