Mathieu functions are frequently encountered in many radiation

scattering and guided wave problems

which are formulated in the elliptic cylindrical coordinate system. Mathieu functions are also used in the studies of the elliptic optical fibre waveguides. Consequently their accurate computation is of general importance. A program flowchart for the computation of Mathieu functions and modified Mathieu functions of the first and second kinds

and some useful expressions for numerical computation are presented

and the related algorithms are discussed. Moreover

some typical tabulated data of Mathieu functions of orders up to 12 with positive and negative parameters q are given to eight significant figures.