The capabilities of the equipment for proton induced X-ray emission analysis at the University of Surrey were examined with particular reference to the trace element analysis of biological samples. The study of samples arising from the Guildford Breast Screening Project was continued. The requirements for trace element analysis of biological samples are outlined together with a review of the available physical analysis techniques. Detail is given of the factors to be considered in order to establish that the study of elemental concentrations by PIXE is feasible. The apparatus used for PIXE analysis is described in detail together with recent improvements to the equipment. The development of a spectrum analysis code HISTO, which simulates the processes of manual analysis, was undertaken. The performance of the code was compared favorably to that of the Ge(Li) spectrum analysis code SAMPO. A preliminary study of 20 samples of human breast cyst fluid was undertaken. The minimum detection limits for those elements assayed by comparative analysis were calculated. The methodology of sample preparation was improved after the examination of target homogeneity and contamination. During a more detailed study of 30 samples the concentration of 9 elements relative to the concetration of potassium was calculated. Calculation of the minimum recommended sample size for elements with Z ≥ 26 indicated that a much larger sample size would be required for reliable results. The PIXE microprobe facility is described and the alignment and operation procedures are outlined. The microprobe was used to examine tree ring samples; examples of some 1D scans are presented. Recommendation that the spectrum analysis code is developed to include a peak location capability is made. Progress with the breast cyst fluid analysis programme is reviewed. The requirement to improve the proton beam current measurment equipment and the data analysis facilities is noted.