The invention relates to a process for producing expandable pelletized material which comprises polylactic acid which comprises the following steps: a) melting and incorporation by mixing of the following components: i) from 50 to 99.9% by weight, based on the total weight of components i to iii), of polylactic acid, ii) from 0 to 49.9% by weight, based on the total weight of components i to iii), of one or more further polymers, iii) from 0.1 to 2% by weight, based on the total weight of components i to iii), of a diepoxide or polyepoxide, and iv) from 0 to 10% by weight of one or more additives, b) incorporation by mixing of v) from 3 to 7% by weight, based on the total weight of components i to iv), of an organic blowing agent into the polymer melt by means of a static or dynamic mixer at a temperature of at least 140° C., c) discharging through a die plate with holes, the diameter of which at the exit from the die is at most 1.5 mm, and d) pelletizing the melt comprising blowing agent directly downstream of the die plate, and under water, at a pressure in the range from 1 to 20 bar. The invention further relates to expandable pelletized material which comprises polylactic acid and which is obtainable by said process, and also to specific expandable pelletized material which comprises polylactic acid and which has a proportion of from 3 to 7% by weight of an organic blowing agent, preferably n-pentane and particularly preferably isopentane. The invention further relates to a preferred process for producing expandable pelletized material which comprises blowing agent and which comprises polylactic acid, and which has low bulk density.