A method for providing an encapsulated flavorant or chemesthetic agent in a smoking article includes forming an emulsion including: (i) a first aqueous solution, comprising one or more cross-linkable polysaccharides; and (ii) a hydrophobic additive comprising one or more flavorants or chemesthetic agents. The method also includes extruding the emulsion into a second aqueous solution in the form of an elongated structure, cross-linking at least a portion of the one or more cross-linkable polysaccharides, removing the cross-linked elongated structure from the second aqueous solution, introducing the cross-linked elongated structure into a filter, or into a rod including a smoking composition, or both; and forming the filter or the rod of the smoking composition into a smoking article. The method can include a drying step.