A method for making an elastic core yarn comprising the steps of: - prearranging a source of an elastic core comprising an elastic fibre made of a natural rubber containing more than 80% of cis-1,4-polyisoprene, wherein said elastic fibre has a linear mass density set between 200 dtex and 1000 dtex; - prearranging at least one covering yarn comprising cotton at a weight percentage higher than 50%, wherein said covering yarn has a linear mass density set between 6 Nm and 100 Nm, said covering yarn twisted with an initial twist direction selected between "Z" and "S"; - conveying said elastic core and said covering yarn up to a collecting spool, at respective predetermined conveying speeds, wherein said conveying speed of said elastic core ranges - from an initial speed, at said source of said elastic core, - to a final speed at least twice said initial speed, at said collecting spool, wherein said step of conveying is carried out in such a way that said covering yarn laterally attains a proximity of said elastic core in a wrapping space; - helically wrapping said covering yarn about said elastic core in said wrapping space, thus obtaining said elastic core yarn; wherein said conveying speeds are selected in such a way that, in said step of helically wrapping: - said covering yarn becomes twisted with a final twist direction opposite to said initial twist direction, i.e. selected between "S" and "Z", respectively; - a number T of coils of said covering yarn set between a predetermined minimum value T 0 and a predetermined maximum value T 1, said minimum and maximum values T 0,T 1 depending upon said linear mass density Nm, is wrapped about one length unit of said elastic core yarn, wherein said wrapping space is a protected space enclosed by a container. - prearranging a source of an elastic core comprising an elastic fibre made of a natural rubber containing more than 80% of cis-1,4-polyisoprene, wherein said elastic fibre has a linear mass density set between 200 dtex and 1000 dtex; - prearranging at least one covering yarn comprising cotton at a weight percentage higher than 50%, wherein said covering yarn has a linear mass density set between 6 Nm and 100 Nm, said covering yarn twisted with an initial twist direction selected between "Z" and "S"; wherein said covering yarn has a linear mass density set between 6 Nm and 100 Nm, said covering yarn twisted with an initial twist direction selected between "Z" and "S"; - conveying said elastic core and said covering yarn up to a collecting spool, at respective predetermined conveying speeds, wherein said conveying speed of said elastic core ranges - from an initial speed, at said source of said elastic core, - to a final speed at least twice said initial speed, at said collecting spool, wherein said step of conveying is carried out in such a way that said covering yarn laterally attains a proximity of said elastic core in a wrapping space; wherein said conveying speed of said elastic core ranges - from an initial speed, at said source of said elastic core, - to a final speed at least twice said initial speed, at said collecting spool, - from an initial speed, at said source of said elastic core, - to a final speed at least twice said initial speed, at said collecting spool, wherein said step of conveying is carried out in such a way that said covering yarn laterally attains a proximity of said elastic core in a wrapping space; - helically wrapping said covering yarn about said elastic core in said wrapping space, thus obtaining said elastic core yarn; - said covering yarn becomes twisted with a final twist direction opposite to said initial twist direction, i.e. selected between "S" and "Z", respectively; - a number T of coils of said covering yarn set between a predetermined minimum value T 0 and a predetermined maximum value T 1, said minimum and maximum values T 0,T 1 depending upon said linear mass density Nm, is wrapped about one length unit of said elastic core yarn,