VTMOP is a Fortran 2008 software package containing two Fortran modules for solving computationally expensive bound-constrained blackbox multiobjective optimization problems. VTMOP implements the algorithm of Deshpande et al. [2016], which handles two or more objectives, does not require any derivatives, and produces well-distributed points over the Pareto front. The first module contains a general framework for solving multiobjective optimization problems by combining response surface methodology, trust region methodology, and an adaptive weighting scheme. The second module features a driver subroutine that implements this framework when the objective functions can be wrapped as a Fortran subroutine. Support is provided for both serial and parallel execution paradigms, and VTMOP is demonstrated on several test problems as well as one real-world problem in the area of particle accelerator optimization.Published version