The　nonlocal　scale　parameter　of　nonlocal　Euler-Bernoulli　beam　theory　is　evaluated　for　the　static　bending　of　single-layer　molybdenum　disulfide　(SLMoS2)　without　predetermined　bending　rigidity.　The　evaluation　is　performed　by　matching　the　fitted　curve　between　the　maximum　deflection　and　the　beam　length　obtained　from　molecular　mechanics　simulations.　It　was　observed　that　the　fitted　curves　have　an　abnormal　sign　in　the　second-order　term　of　the　maximum　deflection　for　SLMoS2,　opposite　to　that　for　graphene　and　regardless　of　the　interatomic　interaction　potentials　used.　Based　on　the　nature　of　＇nonlocal＇　and　the　phenomenological　point　of　view,　a　modified　nonlocal　constitutive　relation　with　a　positive　sign　in　front　of　the　higher-order　term　is　suggested　for　SLMoS2.　The　nonlocal　parameter　and　the　bending　rigidity　of　SLMoS2　are　finally　extracted,　and　the　effect　of　the　nonlocal　scale　parameter　on　the　bending　response　for　SLMoS2　is　found　to　be　significant　for　beam　length　less　than　a　critical　length,　depending　on　both　the　interatomic　interaction　potentials　and　the　boundary　conditions.　Our　new　perspective　should　be　useful　for　researchers　who　are　interested　in　the　engineering　application　of　graphene-like　quasi-two-dimensional　nanostructures　using　nonlocal　beam　theories.　©　2017　IOP　Publishing　Ltd.