Bag (1) for conditioning a biological substance, such as animal semen, which is formed by two walls (10, 11) of plastic material joined so as to delimit a bag (P) for receiving said substance, and comprising, communicating with this bag (P), a conduit (15) for filling, this sack on the other hand comprising at least one pair of openings (3, 4) arranged on either side of said conduit (15), for its suspension, by these openings, to the two complementary fingers of a support, having one (4) at least of these openings (3, 4) an oblong shape and comprising an area (42； 43) forming a hard point, in the one with a reduced width, characterized in that said oblong opening (3, 4) extends perpendicularly to said filling duct (15), because the two openings (3, 4) are arranged in said sack (1) so that the shortest wheelbase (d) between them corresponds to the separation n relative between the two fingers of the support from which said sack (1) is intended to be suspended, and because the length of the oblong opening (4) is greater than the dimension of the finger of the support on which it is intended to be introduced .Saquito (1) de acondicionamiento de una sustancia biológica, tal como semen animal, que está formado por dos paredes (10, 11) de material plástico unidas de manera que delimiten una bolsa (P) de recepción de dicha sustancia, y que comprende, comunicando con esta bolsa (P), un conducto (15) para su rellenado, comprendiendo este saquito por otro lado por lo menos un par de aberturas (3, 4) dispuestas a uno y otro lado de dicho conducto (15), para su suspensión, por estas aberturas, a los dos dedos complementarios de un soporte, teniendo una (4) por lo menos de estas aberturas (3, 4) una forma oblonga y comprendiendo una zona (42； 43) que forma un punto duro, en la que presenta una anchura reducida, caracterizado por que dicha abertura (3, 4) de forma oblonga se extiende perpendicularmente a dicho conducto de rellenado (15), por que las dos aberturas (3, 4) están dis
