A model of filaments of the twist-grain-boundary smectic-A phase (TGBA) arising from the homeotropic smectic-A phase and nucleating on the sample surface is proposed. The model is based on the concept of finite blocks of parallel smectic layers forming a helical structure. The blocks are surrounded by dislocation loops. The model describes the filament structure near the sample surface and the observed inclination of the filament axis with respect to the easy direction of the molecular anchoring on the surface. The model is based on the observations of filament textures of the TGBA phase in a chiral liquid crystalline compound, but can be applied for forming of TGBA filaments in any compound. The compression modulus of the compound has been estimated using such parameters as anchoring energy, estimated from the field necessary to transform the structure into the homeotropic smectic-A.