A high strength hot rolled steel sheet with good formability, which has good magnetic properties, excellent punchability, and a tensile strength of 780 MPa or more. The high strength hot rolled steel sheet having a chemical composition containing C: 0.070% to 0.140%, Si: 0.10% to 1.00%, Mn: 1.00% to 1.80%, P: 0.050% or less, S: 0.0050% or less, N: 0.0080% or less, Al: 0.010% to 0.100%, Ti: 0.050% to 0.150%, and the remainder composed of Fe and incidental impurities, on a percent by mass basis, and 95% or more of bainite microstructure on a volume fraction basis, wherein carbides constituting 80% or more of total precipitation carbides are dispersed at grain boundaries of bainitic ferrite constituting the bainite microstructure and 80% or more of total precipitation carbides have particle grain sizes of 20 to 300 nm.