In many physical and chemical applications one is faced with the problem of calculating the solution of a Fredholm integral equation of the first kind from noisy experimental data. For such problems a solution method based on Tikhonov regularization together with the computer program FTIKREG is presented. In contrast to other solution methods which are based on Tikhonov regularization especially the determination of the regularization parameter has been improved. This improvement leads to much better results, because the error of the result depends mainly on the regularization parameter. Also the numerical effort needed for the corresponding calculation is small for the proposed method. As a consequence many problems can be solved with the program FTIKREG on a personal computer. In order to illustrate the most important features of the solution method, the program FTIKREG is applied to simulated data.