To better understand the decay of vertically polarised fast kink modes of coronal loops by the mechanism of wave tunneling, simulations are performed of fast kink modes in straight flux slabs which have Alfvén speed profiles which include a tunneling region. The decay rates are found to be determined by the mode number of the trapped mode and the thickness of the tunneling region. Two analytical models are suggested to explain the observed decay. The first is a extension of the work of Roberts (1981, Sol. Phys., 69, 39) to include a finite thickness tunneling region, and the second is a simpler model which yields an analytical solution for the relationship between decay rate, period and the thickness of the tunneling region. The decay rates for these straight slabs are found to be slower than in observations and those found in a previous paper on the subject by Brady & Arber (2005, A&A, 438, 733) using curved flux slabs. It is found that the diﬀerence between the straight slabs used here and the curved slabs used in Brady & Arber (2005, A&A, 438, 733) can be represented as a geometric correction to the decay rate.\u
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