diff --git a/src/lp_sensitivity2.jl b/src/lp_sensitivity2.jl
index 3b0d62aa1fb..74e91f66d5d 100644
--- a/src/lp_sensitivity2.jl
+++ b/src/lp_sensitivity2.jl
@@ -334,11 +334,15 @@ end
 Return `true` if `model` is a linear program.
 """
 function _is_lp(model::GenericModel)
+    AffType = Union{GenericVariableRef,GenericAffExpr}
+    if !(objective_function_type(model) <: AffType)
+        return false
+    end
     for (F, S) in list_of_constraint_types(model)
         # TODO(odow): support Interval constraints.
         if !(S <: Union{MOI.LessThan,MOI.GreaterThan,MOI.EqualTo})
             return false
-        elseif !(F <: Union{GenericVariableRef,GenericAffExpr})
+        elseif !(F <: AffType)
             return false
         end
     end
diff --git a/test/test_lp_sensitivity2.jl b/test/test_lp_sensitivity2.jl
index 19d33bb43ff..3931dd6b7f8 100644
--- a/test/test_lp_sensitivity2.jl
+++ b/test/test_lp_sensitivity2.jl
@@ -588,4 +588,39 @@ function test_degenerate_error()
     return
 end
 
+function test_is_lp()
+    err = ErrorException(
+        """
+        Unable to compute LP sensitivity because the model is not a linear program, or it contains interval constraints.
+
+        Remove any nonlinear or integer components, and replace any interval constraints with separate upper and lower bound constraints.
+        """,
+    )
+    # Integer variable
+    model = Model()
+    @variable(model, x, Int)
+    @test_throws err lp_sensitivity_report(model)
+    # Quadratic objective
+    model = Model()
+    @variable(model, x)
+    @objective(model, Min, x^2)
+    @test_throws err lp_sensitivity_report(model)
+    # Nonlinear objective
+    model = Model()
+    @variable(model, x)
+    @objective(model, Max, log(x))
+    @test_throws err lp_sensitivity_report(model)
+    # Quadratic constraint
+    model = Model()
+    @variable(model, x)
+    @constraint(model, x^2 <= 1)
+    @test_throws err lp_sensitivity_report(model)
+    # Conic constraint
+    model = Model()
+    @variable(model, x[1:3])
+    @constraint(model, x in MOI.ExponentialCone())
+    @test_throws err lp_sensitivity_report(model)
+    return
+end
+
 end  # module