The application of inductively-coupled plasma (ICP) spectrometry for the analysis of solutions and slurries is reviewed. The critical parameters which affect analytical performance are identified and methods for the optimisation of the ICP for such applications demonstrated. Particle size of the suspended sample is shown to be the most important factor in the analysis of slurry samples. It is demonstrated that only particles less than 8 um in diameter reach the plasma even when the maximal diameter injector tube (3 mm i.d.) is used. Accordingly various methods for the reduction of particle size have been investigated and milling shown to be the preferable approach. A low cost method using blown zirconia spheres in a screw-cap plastic bottle agitated on a flask shaker was developed. Using this method it proved possible to analyse a wide variety of solid samples using slurry atomisation using both ICP- atomic emission spectrometry (ICP-AES) and ICP-mass spectrometry (ICP-MS) with aqueous calibration. Results are presented for the elemental analysis of certified reference material (CRM) soils, catalyst samples, a zeolite, titanium dioxide, P.T.F.E. powder, and unfiltered natural waters by slurry atomisation ICP-AES. Comparison by other techniques showed excellent accuracy for major, minor and trace elements and equivalent precision to solution analysis. The CRM soils, catalysts and the zeolite were also analysed by ICP-MS using slurry atomisation with similar success and enhanced accuracy at the trace level. Aluminium proved to be an exception and generally low recoveries (80-90%) were observed for this element using slurry atomisation. Finally the uses of the simplex optimisation algorithm to improve analytical performance, particularly in ICP-AES, is discussed. A computer program to facilitate the use of simplex optimisation for a variety of instrumentation was written and its use in three different analytical techniques demonstrated. The necessary hardware and software modifications to a commercially available ICP spectrometer to enable automated simplex optimisation are described. The prospects for such intelligent self-optimising instrumentation are discussed as is the potential extension of the application of slurry analysis by ICP-AES and ICP-MS.