Hinckley and Bosworth council said the tips took place over the weekend (29th/30th January).
Hazardous asbestos was fly-tipped in Veros Lane, Nailstone on Friday and on Green Lane, Odstone on Saturday. A specialist crew will be safely removing the waste as soon as possible.
Although harmless when in one piece, asbestos dust can be very dangerous if inhaled. It's also expensive for the council to clean up.
Fly tipping incidents have increased by 41% in the past year according to Lisa Kirkby, Senior Clean Neighbourhoods officer for the council.
The council asks if anyone has any information to please contact the clean neighbourhoods team on 01455 255971 or on their website https://hinckley-bosworth.gov.uk/flytipping
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