Graphene membranes suspended off electric contacts or other rigid supports are prone to elastic strain, which is concentrated at the edges and corners of the samples. Such a strain leads to an algebraically varying effective magnetic field that can reach a few Tesla in sub-micron wide flakes. In the quantum Hall regime the interplay of the effective and the physical magnetic fields causes backscattering of the chiral edge channels, which can destroy the quantized conductance plateaus.PACS numbers: 73.61. Wp, 73.43.Cd, 73.23.Ad The isolation of graphene monolayers [1,2] and the observation of the integer quantum Hall effect (QHE) in these systems [3,4] have made graphene a very active research topic [5,6]. The integer QHE in graphene is remarkably robust and can be seen even at room temperature [7]. The traditional setup to measure the quantized Hall plateaus involves at least four contacts: source and drain for the current, and two (or more) side contacts for the voltage. This scheme helps to eliminate the spurious contact resistance. The much higher mobility of suspended samples [8-10] raised hopes for observing also the fractional QHE in graphene. Yet demonstrating even the integer QHE in a four-contact setup proved to be difficult in such samples. Only recently the integer QHE has been confirmed in suspended graphene [9,11,12] by reverting to a two-contact scheme. (Similar observations have been made for bilayers [13].) The fractional QHE has also been reported in these experiments [11,12]. An artifact of the two-contact setup is the suppression of the quantized conductance [11,12], familiar from the QHE in semiconductors [14][15][16][17]. The reason why the nominally superior multi-contact scheme is less successful in suspended graphene has not been fully clarified, except for one theory that in small samples the side contacts had to be placed too close to the source and drain, causing admixture of the longitudinal and Hall conductances [11].In this paper we consider a different effect, which may also contribute to the lack of quantization: when the graphene sheet is under tension, the side contacts induce a long-range elastic deformation which acts as a pseudomagnetic field B(x, y) for its massless charge carriers [5,18,19]. The tension can be generated either by the electrostatic force of the underlying gate [20,21], by interaction of graphene with the side walls [22], or as a result of thermal expansion [23,24]. Our main results are as follows. We show that B is concentrated near the corners of the contacts where it exhibits power-law singularities. It decays into the interior of the sample but for a reasonable 0.1% average strain in a 200-nm wide strip, B can remain of the order of a Tesla across its entire width. This leads to backscattering of the QHE edge states when the real magnetic field B is in a similar range, causing the erosion of the quantized conductance plateaus. We give an analytical argument that predicts that the QHE plateaus are destroyed above a threshold Landau level index N c and t...