In geodesy, orthometric and normal heights are considered as basic height systems on the earth. The reference surfaces for these heights are the geoid and quasigeoid respectively. Taking advantage of GNSS measurements, one can achieve a precise solution for the geoid and for the quasigeoid. Two methods, called direct and indirect, are worked out in this research for the computation of separation between geoid and quasigeoid in a mountainous region in the USA. The area selected for this purpose is mountainous and rough enough in order to be able to show the effect of roughness of topography in the sought quantity. The results of the two methods and testing them against GNSS-Levelling on 445 known points indicates an accuracy of 1.3 cm in RMS scale with the direct method, where there is 7 cm as an average difference between the observed geoid and quasigeoid separation and the same quantity derived from the direct method. Using Chi-squared goodness of fit test showed that the distribution of the residual quantities are normally distributed in the test area.