Abstract: This paper aims at investigating some problems in regional numerical weather prediction, such as the errors caused by conventional artificial boundary conditions and their related computational problems, etc. In the first place, the errors caused by the so-called "fixed boundary condi-Lion" employed for making predictions by using the advection equation, are discussed. The corresponding error equation and its solutions are given. It is shown that under this condition the errors propagate towards the central part of the tomputational domain from the boundaries with wind speed u. In f-he vicinity of the inflow boundary, the errors flatten the marching wave. But, on the contrary, in the vicinity of the outflow boundary, the wave amplifies in amplitude abruptly at the time t(= 3Λ/4 u) after the start of computation, where Λ is the wave length. At the same time, the wave becomes much narrower than that at the initial instant. In solving the shallow water equations under the condition, there are two kinds of error propagating towards the interior part of the domain at speeds of |u+c| and |u-c|,respectively, where c is the veloctiy of the external gravity wave.