The constrained interpolation profile (CIP) method is proposed in the field of computational fluid dynamics, because this method is less influenced by numerical dispersions and is stable with an arbitrary time step. In this paper, the CIP method is applied to room acoustic problems, in which boundary modeling and spatial/time discretization are specifically examined. First, frequency-independent and frequency-dependent boundary conditions are introduced and validated with an acoustic tube problem. Second, in one-dimensional and three-dimensional closed sound fields, this paper shows that errors in waveforms and reverberation times using the CIP method are smaller than those using the finite difference time domain method even if the steps for time and space are larger. Third, to deal with complicated shapes, the cubic interpolation with volume/area coordinates (CIVA) method using arbitrary triangular elements is introduced; in two-dimensional sound fields, calculation of the CIVA method is stable even if the quality of triangular elements is low.