The radiative properties of individual mechanical normal modes of vibration of a violin can be calculated from experimental modal analysis results using boundary element radiation programs that integrate the Helmholtz equation over all surface elements. This technique, applied to modal analysis results for a violin with and without a soundpost, helps elucidate the acoustic effects of removal of the soundpost both in terms of the radiation efficiency and directivity of the resultant radiation from each mode and the overall acoustic response. Consonant with the experience of players and luthiers, soundpost removal has a major effect on the predicted acoustic response of the violin. Some violin corpus (sans tailpiece and neck-fingerboard) modes that radiate strongly with the soundpost in place show a substantial change in acoustic response when the soundpost is removed, which is dependent either on the strength of their mechanical excitation and/or their radiation efficiency [G. Bissinger, J. Acoust. Soc. Am. 97, 3154--3164 (1995)]. Particular attention is paid to the predicted acoustic response changes of the first corpus bending modes at 500 Hz.