The translational addition theorems for spherical wave functions are used to develop solutions for nonaxisymmetric acoustic field problems involving nonconcentric spherical boundaries. The forms of the addition theorems are discussed along with their use for translating modal expansions of spherical wave functions centered on one origin to another. In a typical problem involving a number of arbitrarily positioned spherical sources within a spherical‐shaped region, an infinite set of equations for the modal expansion coefficients is developed. This set must be truncated and then solved numerically. Assuming lossless media, comparison of the near‐field and far‐field‐radiated acoustic power provides a test of the accuracy of the numerical results. Other quantities of interest such as the radiation impedance of each source, including the mutual effects of all the other sources, and directivity patterns can be readily computed once a sufficient number of modal coefficients have been computed. In a companion paper [S. A. Lease and W. Thompson, Jr., J. Acoust. Soc. Am.90, xxx–xxx (1991)] numerical results are presented for the specific case of two identical monopole sources within a fluid sphere that is embedded in another infinite fluid medium.