A stochastic computational scheme is developed for investigating formation of trapped (isolated) pore volume in a structure of growing particles, with particle growth occurring only on surface elements exposed to the connected (accessible) part of the pore space. The simulation procedure combines a gradual increase of the particle size with a random walk scheme, the latter used to determine whether a randomly chosen point in the unit cell of the two-phase structure lies in the particle phase or in the connected or isolated part of the matrix phase. The formulated algorithm is applied to structures of freely overlapping, unidirectional cylinders, and results are obtained both for the volume fractions and the specific surface areas of the accessible and inaccessible parts of the pore phase. The trapped volume results are compared with those obtained for ordinary continuum percolation,that is, for uniformly growing particles.