The use of spectral images in many practical applications is getting more and more common as the cost of computation power and of storage space gets smaller. But like ordinary color images, the spectral images also suffer from noise caused by transmission and manipulation errors. In this study different multidimensional median filtering methods are developed for noise removal from spectral images. First vector median filters are applied to spectral images. Then new three-dimensional median filters are introduced. In experiments we compared three-dimensional filters to common 2D median filters and found out that three-dimensional median filters on average were the best of all applied filters.