We studied the 2-dimensional spectral measurment of short crested irregular water waves in order to understand characteristics of irregular water waves with directional spectra in ocean or model basin. The 2-dimensional spectral estimation depends on cross spectral estimation errors. In this paper, the 2-dimensional spectra estimated by Maximum Liklihood Method (M.L.M.) are discussed from the view point of cross spectral estimation errors. Those errors includs the white noise of a measured time-history and the errors of calibration factor or arrangement of wave probes. We found out that the 2-dimensional spectra estimated by M.L.M. depend strictly on the distance of arrangement of wave probes. According to numerical simulation, moreover, 2-dimensional spectra estimated by M.L.M. are affected directly by the errors of cross spectral estimation.