A graphics processing unit having a shader execution unit for executing a plurality of shader routines in order to perform a predetermined sequence of shader operations. The shader operations include a tessellation operation which receives as inputs tessellation control data and an input list of input data for M input vertices, and generates at least output data for P output vertices. For each output vertex, the controller allocates a tessellation shader routine from the set of shader routines, and the shader execution unit is configured, each time the tessellation shader routine is executed for an associated output vertex: (i) to compute, in dependence on the tessellation control data and the associated output vertex, tessellation coordinate data; and (ii) to compute from the input data for the M input vertices, and the tessellation coordinate data generated in step (i), the output data for the associated output vertex.